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gn in to your account x wordpress.com. Log in x Quizzes & Te ourseld 13273178&OpenVellumHMAC; d73a60f8007665b2d92f169532cf7136 10013 Take a Test https//www.mathxl.com/Student/PlayerTest aspx?testld 150846250&centerwin; yes Fall 2016: MATH 364. Calculus III Section 1 Sydne Test: Final Examination Fall 2016 his Question: 3 pts 9 of 30 (7 complete) Compute the directional derivative of the function fx -2xy y2 at the point p(3, -2 in the direction of the vector (73. The directional derivative is Type an exact answer using radicals abheeded) lal Vi B. (u) More Enter your answer in the answer box Chapter 2 Pre-Test

Explanation / Answer

f(x,y)= -2xy +y2

gradient f =<-2y , -2x +2y>

at (3,-2)

f =<-2*-2 , (-2*3) +(2*-2)>

f =<4 , -10>

given vector u =<7,3>

|u|=(72+32)=50=52

directional derivative =f.u/|u|

directional derivative =<4 , -10>.<7,3>/52

directional derivative =[(4*7)+(-10*3)]/52

directional derivative =-2/52

directional derivative =-(2)/5

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by lagrange multipliers

f=g   

<10x,8y,4z>=<4,3,-8>

10x=4 , 8y=3 , 4z=-8

4x+3y -8z+6=0

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