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Chapter 12: Q. 11 (page 953)

Let f(x)be a function of a single variable. Define the directional derivative of fin the direction of the unit vector u=鉄�伪鉄�at a point c. What are the only possible values for 伪?

Short Answer

Expert verified

The possible value of 伪 is equal to 1.

Step by step solution

01

Introduction

Directional Derivative of a function of single variables:

Let f(x)be a function of single variables defined on an open set containing the point x0, and let u=(伪)be a unit vector at the point c. The directional derivative of fat x0in the direction of u, denoted by Dufx0.

02

Equation

The Equation is,

Dufx0,y0=Limh鈫�0fx0+伪+h-fx0h

Provided that limit is exists.

uis the unit vector, hence the only possible value of 伪is equal to 1.

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Most popular questions from this chapter

Describe the meanings of each of the following mathematical expressions

鈭�w鈭�x

Given a function of n variables, z=fx1,x2,鈥�,xn,and a constraint equation, gx1,x2,鈥�,xn=0,how many equations would we obtain if we tried to optimize f by the method of Lagrange multipliers?

Find the directional derivative of the given function at the specified point P in the direction of the given vector. Note: The given vectors may not be unit vectors.

f(x,y)=yx,P=(4,3),v=鉄�3,鈭�2鉄�

Describe the meanings of each of the following mathematical expressions :

鈭�A

Describe the meanings of each of the following mathematical expressions :

fyx0,y0
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