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update AD5 checkit per CheckIt - AD5 and AD6. #52 (#814)
* update AD5 checkit per CheckIt - AD5 and AD6. #52 * changed answers to list format * changed "region" to "open intervals" * update ad6 checkit per CheckIt - AD5 and AD6. #52 * changed "region" to "open intervals" * formatted answers as list rather than paragraph * Update source/calculus/exercises/outcomes/AD/AD5/template.xml Co-authored-by: Steven Clontz <steven.clontz@gmail.com> * fixed spatext syntax in AD5 and AD6 * remove <p> tags around <list>s * Update source/calculus/exercises/outcomes/AD/AD6/template.xml Co-authored-by: Steven Clontz <steven.clontz@gmail.com> * Update source/calculus/exercises/outcomes/AD/AD6/template.xml Co-authored-by: Steven Clontz <steven.clontz@gmail.com> * Update source/calculus/exercises/outcomes/AD/AD6/template.xml Co-authored-by: Steven Clontz <steven.clontz@gmail.com> --------- Co-authored-by: Steven Clontz <steven.clontz@gmail.com>
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‎source/calculus/exercises/outcomes/AD/AD5/template.xml‎

Lines changed: 130 additions & 31 deletions
Original file line numberDiff line numberDiff line change
@@ -2,58 +2,157 @@
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<knowl mode="exercise" xmlns="https://spatext.clontz.org" version="0.2">
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<intro>
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<p>
5-
For <m>\displaystyle f(x) = {{f}} </m>, identify the regions for which <m>f(x)</m> is increasing and decreasing (if any). Additionally, identify and classify all local extrema.
5+
For <m>\displaystyle f(x) = {{f}} </m>, identify the open intervals for which <m>f(x)</m> is increasing and decreasing (if any). Additionally, identify and classify all local extrema.
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</p>
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</intro>
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<outtro>
1010
<!-- {{#case1}} -->
11-
<p>
12-
We have that <m>\displaystyle f'(x) = {{fp}}</m>.
13-
When <m>x &lt; {{cv1}}, f'(x) {{sign11}}</m> and <m>y</m> is {{change1}}.
14-
When <m>{{cv1}} &lt; x &lt; {{cv2}}, f'(x) {{sign12}}</m> and <m>y</m> is {{change2}}.
15-
When <m>{{cv2}} &lt; x, f'(x) {{sign13}}</m> and <m>y</m> is {{change3}}. There is a critical point <m>{{cp1}}</m> which is neither a max nor min.
16-
</p>
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<list>
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<item>
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<p>
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We have that <m>\displaystyle f'(x) = {{fp}}</m>.
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</p>
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</item>
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<item>
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<p>
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When <m>x &lt; {{cv1}}, f'(x) {{sign11}}</m> and <m>y</m> is {{change1}}.
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</p>
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</item>
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<item>
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<p>
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When <m>{{cv1}} &lt; x &lt; {{cv2}}, f'(x) {{sign12}}</m> and <m>y</m> is {{change2}}.
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</p>
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</item>
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<item>
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<p>
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When <m>{{cv2}} &lt; x, f'(x) {{sign13}}</m> and <m>y</m> is {{change3}}. There is a critical point <m>{{cp1}}</m> which is neither a max nor min.
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</p>
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</item>
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</list>
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<!-- {{/case1}} -->
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<!-- {{#case2}} -->
21-
<p>
22-
We have that <m>\displaystyle f'(x) = {{fp}}</m>.
23-
When <m>x &lt; {{cv1}}, f'(x) {{sign11}}</m> and <m>y</m> is {{change1}}.
24-
When <m>{{cv1}} &lt; x &lt; {{cv2}}, f'(x) {{sign12}}</m> and <m>y</m> is {{change2}}.
25-
When <m>{{cv2}} &lt; x, f'(x) {{sign13}}</m> and <m>y</m> is {{change3}}. There is a critical point <m>{{cp1}}</m> which is a local minimum and a critical point <m>{{cp2}}</m> is a local maximum.
26-
</p>
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<list>
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<item>
42+
<p>
43+
44+
We have that <m>\displaystyle f'(x) = {{fp}}</m>.
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</p>
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</item>
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<item>
48+
<p>
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50+
When <m>x &lt; {{cv1}}, f'(x) {{sign11}}</m> and <m>y</m> is {{change1}}.
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</p>
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</item>
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<item>
54+
<p>
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When <m>{{cv1}} &lt; x &lt; {{cv2}}, f'(x) {{sign12}}</m> and <m>y</m> is {{change2}}.
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</p>
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</item>
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<item>
60+
<p>
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When <m>{{cv2}} &lt; x, f'(x) {{sign13}}</m> and <m>y</m> is {{change3}}. There is a critical point <m>{{cp1}}</m> which is a local minimum and a critical point <m>{{cp2}}</m> is a local maximum.
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</p>
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</item>
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</list>
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<!-- {{/case2}} -->
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<!-- {{#case3}} -->
31-
<p>
32-
We have that <m>\displaystyle f'(x) = {{fp}}</m>.
33-
When <m>x &lt; {{cv1}}, f'(x) {{sign11}}</m> and <m>y</m> is {{change1}}.
34-
When <m>{{cv1}} &lt; x &lt; {{cv2}}, f'(x) {{sign12}}</m> and <m>y</m> is {{change2}}.
35-
When <m>{{cv2}} &lt; x, f'(x) {{sign13}}</m> and <m>y</m> is {{change3}}. There are no critical points.
36-
</p>
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<list>
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<item>
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<p>
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74+
We have that <m>\displaystyle f'(x) = {{fp}}</m>.
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</p>
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</item>
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<item>
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<p>
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When <m>x &lt; {{cv1}}, f'(x) {{sign11}}</m> and <m>y</m> is {{change1}}.
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</p>
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</item>
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<item>
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<p>
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When <m>{{cv1}} &lt; x &lt; {{cv2}}, f'(x) {{sign12}}</m> and <m>y</m> is {{change2}}.
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</p>
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</item>
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<item>
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<p>
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When <m>{{cv2}} &lt; x, f'(x) {{sign13}}</m> and <m>y</m> is {{change3}}. There are no critical points.
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</p>
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</item>
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</list>
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<!-- {{/case3}} -->
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<!-- {{#case4}} -->
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42101
<!-- {{#odd}} -->
43-
<p>
44-
We have that <m>\displaystyle f'(x) = {{fp}}</m>.
45-
When <m>x &lt; {{cv1}}, f'(x) {{sign11}}</m> and <m>y</m> is {{change1}}.
46-
When <m>{{cv1}} &lt; x &lt; {{cv2}}, f'(x) {{sign12}}</m> and <m>y</m> is {{change2}}.
47-
When <m>{{cv2}} &lt; x, f'(x) {{sign13}}</m> and <m>y</m> is {{change3}}. There is a critical point <m>{{cp1}}</m> which is a local minimum.
48-
</p>
102+
<list>
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<item>
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<p>
105+
106+
We have that <m>\displaystyle f'(x) = {{fp}}</m>.
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</p>
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</item>
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<item>
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<p>
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When <m>x &lt; {{cv1}}, f'(x) {{sign11}}</m> and <m>y</m> is {{change1}}.
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</p>
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</item>
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<item>
116+
<p>
117+
118+
When <m>{{cv1}} &lt; x &lt; {{cv2}}, f'(x) {{sign12}}</m> and <m>y</m> is {{change2}}.
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</p>
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</item>
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<item>
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<p>
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124+
When <m>{{cv2}} &lt; x, f'(x) {{sign13}}</m> and <m>y</m> is {{change3}}. There is a critical point <m>{{cp1}}</m> which is a local minimum.
125+
</p>
126+
</item>
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</list>
49128
<!-- {{/odd}} -->
50129
<!-- {{#even}} -->
51-
<p>
52-
We have that <m>\displaystyle f'(x) = {{fp}}</m>.
53-
When <m>x &lt; {{cv1}}, f'(x) {{sign11}}</m> and <m>y</m> is {{change1}}.
54-
When <m>{{cv1}} &lt; x &lt; {{cv2}}, f'(x) {{sign12}}</m> and <m>y</m> is {{change2}}.
55-
When <m>{{cv2}} &lt; x, f'(x) {{sign13}}</m> and <m>y</m> is {{change3}}. There are critical points <m>{{cp1}}</m> which is a local maximum and <m>{{cp2}}</m> which is a local minimum.
56-
</p>
130+
<list>
131+
<item>
132+
<p>
133+
134+
We have that <m>\displaystyle f'(x) = {{fp}}</m>.
135+
</p>
136+
</item>
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<item>
138+
<p>
139+
140+
When <m>x &lt; {{cv1}}, f'(x) {{sign11}}</m> and <m>y</m> is {{change1}}.
141+
</p>
142+
</item>
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<item>
144+
<p>
145+
146+
When <m>{{cv1}} &lt; x &lt; {{cv2}}, f'(x) {{sign12}}</m> and <m>y</m> is {{change2}}.
147+
</p>
148+
</item>
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<item>
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<p>
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152+
When <m>{{cv2}} &lt; x, f'(x) {{sign13}}</m> and <m>y</m> is {{change3}}. There are critical points <m>{{cp1}}</m> which is a local maximum and <m>{{cp2}}</m> which is a local minimum.
153+
</p>
154+
</item>
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</list>
57156
<!-- {{/even}} -->
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‎source/calculus/exercises/outcomes/AD/AD6/template.xml‎

Lines changed: 129 additions & 29 deletions
Original file line numberDiff line numberDiff line change
@@ -2,52 +2,152 @@
22
<knowl mode="exercise" xmlns="https://spatext.clontz.org" version="0.2">
33
<intro>
44
<p>
5-
For <m>\displaystyle f(x) = {{f}} </m>, identify the regions where <m>f(x)</m> is concave up and concave down (if any) as well as all inflection points.
5+
For <m>\displaystyle f(x) = {{f}} </m>, identify the open intervals where <m>f(x)</m> is concave up and concave down (if any) as well as all inflection points.
66
</p>
77
</intro>
88

99
<outtro>
1010
<!-- {{#case1}} -->
11-
<p>
12-
We have that <m>\displaystyle f''(x) = {{fpp}}</m>.
13-
When <m>x &lt; {{cc1}}, f''(x) {{sign21}}</m> and <m>y</m> is {{concave1}}.
14-
When <m>{{cc1}} &lt; x &lt; {{cc2}}, f''(x) {{sign22}}</m> and <m>y</m> is {{concave2}}.
15-
When <m>{{cc2}} &lt; x &lt; {{cc3}}, f''(x) {{sign23}}</m> and <m>y</m> is {{concave3}}.
16-
When <m>{{cc3}} &lt; x, f''(x) {{sign24}}</m> and <m>y</m> is {{change4}}. There are inflection points <m>{{ip1}}</m> and <m>{{ip2}}</m>.
17-
</p>
11+
<list>
12+
<item>
13+
<p>
14+
15+
We have that <m>\displaystyle f''(x) = {{fpp}}</m>.
16+
</p>
17+
</item>
18+
<item>
19+
<p>
20+
21+
When <m>x &lt; {{cc1}}, f''(x) {{sign21}}</m> and <m>y</m> is {{concave1}}.
22+
</p>
23+
</item>
24+
<item>
25+
<p>
26+
27+
When <m>{{cc1}} &lt; x &lt; {{cc2}}, f''(x) {{sign22}}</m> and <m>y</m> is {{concave2}}.
28+
</p>
29+
</item>
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<item>
31+
<p>
32+
33+
When <m>{{cc2}} &lt; x &lt; {{cc3}}, f''(x) {{sign23}}</m> and <m>y</m> is {{concave3}}.
34+
</p>
35+
</item>
36+
<item>
37+
<p>
38+
39+
When <m>{{cc3}} &lt; x, f''(x) {{sign24}}</m> and <m>y</m> is {{concave4}}. There are inflection points <m>{{ip1}}</m> and <m>{{ip2}}</m>.
40+
</p>
41+
</item>
42+
</list>
1843
<!-- {{/case1}} -->
1944

2045
<!-- {{#case2}} -->
21-
<p>
22-
We have that <m>\displaystyle f''(x) = {{fpp}}</m>.
23-
When <m>x &lt; {{cc1}}, f''(x) {{sign21}}</m> and <m>y</m> is {{concave1}}.
24-
When <m>{{cc1}} &lt; x &lt; {{cc2}}, f''(x) {{sign22}}</m> and <m>y</m> is {{concave2}}.
25-
When <m>{{cc2}} &lt; x &lt; {{cc3}}, f''(x) {{sign23}}</m> and <m>y</m> is {{concave3}}.
26-
When <m>{{cc3}} &lt; x, f''(x) {{sign24}}</m> and <m>y</m> is {{change4}}. There are inflection points <m>{{ip1}}</m>, <m>{{ip2}}</m> and <m>{{ip3}}</m>.
27-
</p>
46+
<list>
47+
<item>
48+
<p>
49+
50+
We have that <m>\displaystyle f''(x) = {{fpp}}</m>.
51+
</p>
52+
</item>
53+
<item>
54+
<p>
55+
56+
When <m>x &lt; {{cc1}}, f''(x) {{sign21}}</m> and <m>y</m> is {{concave1}}.
57+
</p>
58+
</item>
59+
<item>
60+
<p>
61+
62+
When <m>{{cc1}} &lt; x &lt; {{cc2}}, f''(x) {{sign22}}</m> and <m>y</m> is {{concave2}}.
63+
</p>
64+
</item>
65+
<item>
66+
<p>
67+
68+
When <m>{{cc2}} &lt; x &lt; {{cc3}}, f''(x) {{sign23}}</m> and <m>y</m> is {{concave3}}.
69+
</p>
70+
</item>
71+
<item>
72+
<p>
73+
74+
When <m>{{cc3}} &lt; x, f''(x) {{sign24}}</m> and <m>y</m> is {{concave4}}. There are inflection points <m>{{ip1}}</m>, <m>{{ip2}}</m> and <m>{{ip3}}</m>.
75+
</p>
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</item>
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</list>
2878
<!-- {{/case2}} -->
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3080

3181
<!-- {{#case3}} -->
32-
<p>
33-
We have that <m>\displaystyle f''(x) = {{fpp}}</m>.
34-
When <m>x &lt; {{cc1}}, f''(x) {{sign21}}</m> and <m>y</m> is {{concave1}}.
35-
When <m>{{cc1}} &lt; x &lt; {{cc2}}, f''(x) {{sign22}}</m> and <m>y</m> is {{concave2}}.
36-
When <m>{{cc2}} &lt; x &lt; {{cc3}}, f''(x) {{sign23}}</m> and <m>y</m> is {{concave3}}.
37-
When <m>{{cc3}} &lt; x, f''(x) {{sign24}}</m> and <m>y</m> is {{change4}}. There is an inflection point <m>{{ip1}}</m>.
38-
</p>
82+
<list>
83+
<item>
84+
<p>
85+
86+
We have that <m>\displaystyle f''(x) = {{fpp}}</m>.
87+
</p>
88+
</item>
89+
<item>
90+
<p>
91+
92+
When <m>x &lt; {{cc1}}, f''(x) {{sign21}}</m> and <m>y</m> is {{concave1}}.
93+
</p>
94+
</item>
95+
<item>
96+
<p>
97+
98+
When <m>{{cc1}} &lt; x &lt; {{cc2}}, f''(x) {{sign22}}</m> and <m>y</m> is {{concave2}}.
99+
</p>
100+
</item>
101+
<item>
102+
<p>
103+
104+
When <m>{{cc2}} &lt; x &lt; {{cc3}}, f''(x) {{sign23}}</m> and <m>y</m> is {{concave3}}.
105+
</p>
106+
</item>
107+
<item>
108+
<p>
109+
110+
When <m>{{cc3}} &lt; x, f''(x) {{sign24}}</m> and <m>y</m> is {{concave4}}. There is an inflection point <m>{{ip1}}</m>.
111+
</p>
112+
</item>
113+
</list>
39114
<!-- {{/case3}} -->
40115

41116

42117
<!-- {{#case4}} -->
43118

44-
<p>
45-
We have that <m>\displaystyle f''(x) = {{fpp}}</m>.
46-
When <m>x &lt; {{cc1}}, f''(x) {{sign21}}</m> and <m>y</m> is {{concave1}}.
47-
When <m>{{cc1}} &lt; x &lt; {{cc2}}, f''(x) {{sign22}}</m> and <m>y</m> is {{concave2}}.
48-
When <m>{{cc2}} &lt; x, f''(x) {{sign23}}</m> and <m>y</m> is {{concave3}}.
49-
There is an inflection point <m>{{ip1}}</m>.
50-
</p>
119+
<list>
120+
<item>
121+
<p>
122+
123+
We have that <m>\displaystyle f''(x) = {{fpp}}</m>.
124+
</p>
125+
</item>
126+
<item>
127+
<p>
128+
129+
When <m>x &lt; {{cc1}}, f''(x) {{sign21}}</m> and <m>y</m> is {{concave1}}.
130+
</p>
131+
</item>
132+
<item>
133+
<p>
134+
135+
When <m>{{cc1}} &lt; x &lt; {{cc2}}, f''(x) {{sign22}}</m> and <m>y</m> is {{concave2}}.
136+
</p>
137+
</item>
138+
<item>
139+
<p>
140+
141+
When <m>{{cc2}} &lt; x, f''(x) {{sign23}}</m> and <m>y</m> is {{concave3}}.
142+
</p>
143+
</item>
144+
<item>
145+
<p>
146+
147+
There is an inflection point <m>{{ip1}}</m>.
148+
</p>
149+
</item>
150+
</list>
51151
<!-- {{/case4}} -->
52152

53153

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