   Chapter 3.1, Problem 81E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Let f ( x ) { x 2   if   x   ≤   2   m x + b   i f   x > 2 Find the values of m and b that make f differentiable everywhere.

To determine

To find: The value of m and b.

Explanation

Given:

The function f(x)={x2if x2mx+b   if x>2.

Derivative Rule:

(1) Power Rule: ddx(xn)=nxn1

(2) Sum rule: ddx(f+g)=ddx(f)+ddx(g)

(3) Constant multiple rule: ddx(cf)=cddx(f)

Calculation:

Obtain the derivative of the function f(x) if x<2.

f(x)=ddx(f(x))=ddx(x2)

Apply the power rule (1) and simplify the terms,

f(x)=2x21=2x

Thus, the derivative of the function f(x) if x<2 is f(x)=2x.

Obtain the derivative of the function f(x) if x>2

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