Chapter 12: Q. 11 (page 953)

Let $f (x)$ be a function of a single variable. Define the directional derivative of $f$ in the direction of the unit vector $u = ⟨ α ⟩$ at a point $c$ . What are the only possible values for $α$ ?

Short Answer

Expert verified

The possible value of $α$ is equal to $1 .$

Step by step solution

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 $(x_{0})$ , and let $u = (α)$ be a unit vector at the point $c$ . The directional derivative of $f$ at $(x_{0})$ in the direction of $u$ , denoted by $D_{u} f (x_{0})$ .

Equation

The Equation is,

$D_{u} f (x_{0}, y_{0}) = {Lim}_{h \to 0} \frac{f (x_{0} + α + h) - f (x_{0})}{h}$

Provided that limit is exists.

u

is the unit vector, hence the only possible value of

α

is equal to

1 .

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Let $f (x)$ be a function of a single variable. Define the directional derivative of $f$ in the direction of the unit vector $u = ⟨ α ⟩$ at a point $c$ . What are the only possible values for $α$ ?

Short Answer

Step by step solution

Introduction

Equation

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

Short Answer

Step by step solution

Introduction

Equation

One App. One Place for Learning.

Most popular questions from this chapter

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Let $f (x)$ be a function of a single variable. Define the directional derivative of $f$ in the direction of the unit vector $u = ⟨ α ⟩$ at a point $c$ . What are the only possible values for $α$ ?