Added question 7

Author: Programatic

MultiTest2.log

@@ -1,4 +1,4 @@
-This is pdfTeX, Version 3.14159265-2.6-1.40.19 (MiKTeX 2.9.6840 64-bit) (preloaded format=pdflatex 2018.10.28)  18 DEC 2018 19:09
+This is pdfTeX, Version 3.14159265-2.6-1.40.19 (MiKTeX 2.9.6840 64-bit) (preloaded format=pdflatex 2018.10.28)  18 DEC 2018 19:25
 entering extended mode
 **./MultiTest2.tex
 (MultiTest2.tex
@@ -109,7 +109,7 @@ Here is how much of TeX's memory you used:
  4779 multiletter control sequences out of 15000+200000
  9641 words of font info for 35 fonts, out of 3000000 for 9000
  1141 hyphenation exceptions out of 8191
- 27i,7n,21p,208b,254s stack positions out of 5000i,500n,10000p,200000b,50000s
+ 27i,7n,21p,208b,252s stack positions out of 5000i,500n,10000p,200000b,50000s
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 onts/type1/public/amsfonts/cm/cmex10.pfb><D:/Users/fordm/AppData/Local/Programs
@@ -121,7 +121,7 @@ D:/Users/fordm/AppData/Local/Programs/MiKTeX 2.9/fonts/type1/public/amsfonts/cm
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-Output written on MultiTest2.pdf (3 pages, 92042 bytes).
+Output written on MultiTest2.pdf (3 pages, 92557 bytes).
 PDF statistics:
  48 PDF objects out of 1000 (max. 8388607)
  0 named destinations out of 1000 (max. 500000)

MultiTest2.pdf

@@ -39,7 +39,11 @@
 $$\vec{n_1} = <4,-2,4> \quad \vec{n_2} = <-4, 2,1>$$
 $$\cos(\theta) = \frac{\vec{n_1} \cdot \vec{n_2}}{\parallel \vec{n_1} \parallel \cdot \parallel \vec{n_2} \parallel}$$
 $$\cos(\theta) = \frac{-16}{6\sqrt{21}}$$
-\item a
+\item $$f\left(x,y,z\right)=x^3+y^2-z^3 \quad f\left(9,10,12\right) = -899$$
+$$f_x = 3x^2 \quad f_y = 3y^2 \quad f_z = -3z^2$$
+$$L(9,10,12) = f(9,10,12) + f_x(x-9)+f_y(y-10)+f_z(z-12)$$
+$$L(9,10,12) = -788$$
+
 \item $$<\frac{3}{5}, \frac{4}{5}> \cdot \nabla f = 2 \quad <\frac{-4}{5}, \frac{3}{5}> \cdot \nabla f = 2$$
 $$\frac{3}{5}f_x+\frac{4}{5}f_y=2 \quad \frac{-4}{5}f_x+\frac{3}{5}f_y=-1$$
 $$f_x (0,0) = 2 \quad f_y(0,0)=1$$