# Transcribed Image Text: point P are given. Let 0 correspond to the direction of the directional derivative. a. Find the gradient and evaluate it at P. b. Find the angles 0

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find the maximum value. e. Verify that the value of 0 that maximizes g corresponds to the direction of the gradient. Verify that the maximum value of g equals the magnitude of the gradient. |38. (х, у) — 8 + х + 3у?; Р(-3, —1) |

Transcribed Image Text: point P are given. Let 0 correspond to the direction of the directional

derivative.

a. Find the gradient and evaluate it at P.

b. Find the angles 0 (with respect to the positive x-axis) associated

with the directions of maximum increase, maximum decrease, and

zero change.

c. Write the directional derivative at P as a function of 0; call ts

function g.

d. Find the value of 0 that maximizes g(0) and find the maximum

value.

e. Verify that the value of 0 that maximizes g corresponds to the

direction of the gradient. Verify that the maximum value of g equals

the magnitude of the gradient.

|38. (х, у) — 8 + х + 3у?; Р(-3, —1)

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