Section 11.6: Problem 20 Previous Problem List Next (1 point) Use the contour di
ID: 2888658 • Letter: S
Question
Section 11.6: Problem 20 Previous Problem List Next (1 point) Use the contour diagram for f(x, y) shown below to estimate the directional derivative of f in the direction v at the point P. (2, 2) in the direction j, the directional derivative is (a) At the point P approximately (b) At the point P approximately (3, 2) in the direction -i, the directional derivative is (i j)/2, the directional derivative (c) At the point P (4,1) in the direction v- is approximately (1, 0) in the direction -i, the directional derivative is (d) At the point P approximately Note: You can earn partial credit on this problem. Preview My Answers Submit AnswersExplanation / Answer
(a)
gradiant,f(2,2)= ((6-4)/(3-2))i +((6-4)/(3-2))j
f(2,2)= 2i +2j
v =0i+1j
|v|=1
directional derivative =f. v/|v|
directional derivative =(2i +2j)(0i +1j)
directional derivative =(2*0)+(2*1)
directional derivative =2
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(b)
gradiant,f(3,2)= ((8-6)/(4-3))i +((8-6)/(2.6-2))j
f(3,2)= 2i +(10/3)j
v =-1i+0j
|v|=1
directional derivative =f. v/|v|
directional derivative =(2i +(10/3)j)(-1i +0j)
directional derivative =(2*-1)+((10/3)*0)
directional derivative =-2
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(c)
gradiant,f(4,1)= ((4-2)/(4-2))i +((4-2)/(1-0.5))j
f(4,1)= 1i +4j
v =(1i+1j)/2
|v|=1
directional derivative =f. v/|v|
directional derivative =(1i +4j)(1i+1j)/2
directional derivative =((1*1)+(4*1))/2
directional derivative =5/2
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(d)
gradiant,f(1,0)= 0i +((2-0)/(2-0))j
f(3,2)= 0i +1j
v =-1i+0j
|v|=1
directional derivative =f. v/|v|
directional derivative =(0i +1j)(-1i +0j)
directional derivative =(0*-1)+(1*0)
directional derivative =0+0
directional derivative =0
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