Determine whether f is differentiable at x=0 by considering limh→0f(0+h)−f(0)h. f(x)=18−x Choose the correct answer below. A. The function f is not differentiable at x=0 because the left- and right-hand limits of the difference quotient do not exist at x=0.

Determine whether f is differentiable at x=0 by considering limh→0f(0+h)−f(0)h. f(x)=18−x Choose the correct answer below. A. The function f is not differentiable at x=0 because the left- and right-hand limits of the difference quotient do not exist at x=0.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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Question

Determine whether f is differentiable at

x=0

by considering

limh→0f(0+h)−f(0)h.

f(x)=18−x

Choose the correct answer below.

The function f is not differentiable at

x=0

because the left- and right-hand limits of the difference quotient do not exist at

x=0.

The function f is not differentiable at

x=0

because the left- and right-hand limits of the difference quotient exist at

x=0,

but are not equal.

The function f is differentiable at

x=0

because the graph has a sharp corner at

x=0.

The function f is differentiable at

x=0

because both the left- and right-hand limits of the difference quotient exist at

x=0.

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Determine whether f is differentiable at x=0 by considering limh→0f(0+h)−f(0)h. ​f(x)=18−x Choose the correct answer below. A. The function f is not differentiable at x=0 because the​ left- and​ right-hand limits of the difference quotient do not exist at x=0.

Determine whether f is differentiable at x=0 by considering limh→0f(0+h)−f(0)h. f(x)=18−x Choose the correct answer below. A. The function f is not differentiable at x=0 because the left- and right-hand limits of the difference quotient do not exist at x=0.