Let Find the directions u and the values of Duf(1,-1) for

Chapter 13, Problem 29E

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Theory and Examples

Let $f(x, y)=x^{2}-x y+y^{2}-y$. Find The directions u and the values of $D_{u} f(1,-1)$ for which

a. $D_{u} f(1,-1)$ is largest

b. $D_{u} f(1,-1)$ is smallest

c. $D_{u} f(1,-1)=0$

d. $D_{u} f(1,-1)=4$

e. $D_{u} f(1,-1)=-3$

Equation Transcription:

$f(x,y)={x}^{2}-xy+{y}^{2}-y$

${D}_{u}\ f(1,-1)$

${D}_{u}\ f(1,-1)\ =\ 0$

${D}_{u}\ f(1,-1)\ =\ 4$

${D}_{u}\ f(1,-1)\ =\ -3$

Text Transcription:

f(x,y)=x2-xy+y2-y

D_u f(1,-1)

D_u f(1,-1)= 0

D_u f(1,-1) = 4

D_u f(1,-1)= -3

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