   Chapter 3.2, Problem 44E ### 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

# Suppose that f(4) = 2, g(4) = 5, f'(4) = 6. and g'(4) = –3. Find h'(4).(a) h(x) = 3f(x) + 8g(x)(b) h(x) = f(x)g(x)(c) h ( x ) = f ( x ) g ( x ) (d) h ( x ) = g ( x ) f ( x ) + g ( x )

(a)

To determine

To find: The value of h(4) when h(x)=3f(x)+8g(x).

Explanation

Given:

The values are f(4)=2,f(4)=6,g(4)=5 and g(4)=3.

Derivative rule:

(1) Product Rule: ddx[f1(x)f2(x)]=f1(x)ddx[f2(x)]+f2(x)ddx[f1(x)]

(2) Quotient Rule: If f1(x) and f2(x) are both differentiable, then

ddx[f1(x)f2(x)]=f2(x)ddx[f1(x)]f1(x)ddx[f2(x)][f2x]2

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

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

Calculation:

Obtain the value of h(x)

(b)

To determine

To find: The value of h(4) when h(x)=f(x)g(x).

(c)

To determine

To find: The value of h(4) when h(x)=f(x)g(x).

(d)

To determine

To find: The value of h(4) when h(x)=g(x)f(x)+g(x).

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