   Chapter 14, Problem 44RE

Chapter
Section
Textbook Problem

(a) When is the directional derivative of f a maximum?(b) When is it a minimum?(c) When is it 0?(d) When is it half of its maximum value?

(a)

To determine

To find: The directional derivative of f attains its maximum value.

Explanation

Theorem used:

“Suppose f is differentiable function of two or three variables. The maximum value of the directional derivative Duf(x) is |f(x)| and it occurs when u has the same direction as the gradient vector f(x) .”

Calculation:

Consider the function f is differentiable function of three variables.

The gradient vector of the function f(x,y,z) is f(x,y,z) .

The directional derivative of f(x,y,z) in the direction of the unit vector u=a,b,c is,

Duf(x,y,z)=f(x,y,z)u=|f</

(b)

To determine

To find: The directional derivative of f attains its minimum value.

(c)

To determine

To find: The directional derivative of f attains its value is 0.

(d)

To determine

To find: The directional derivative of f attains its half of maximum value.

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Calculate y'. 44. y=sinmxx

Single Variable Calculus: Early Transcendentals, Volume I

In Exercises 2528. solve the equation by factoring. 25. 8x2 + 2x 3 = 0

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Given Q=CV,C=12, and V=2500, find Q.

Elementary Technical Mathematics

Find the area enclosed by the curve r2 = 9 cos 5.

Single Variable Calculus: Early Transcendentals

Let f(x)={2x2forx13forx1. Which limit does not exist? a) limx3f(x) b) limx1+f(x) c) limx1f(x) d) limx1f(x)

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 