   Chapter 9.8, Problem 1E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In Problems 1-6, find the second derivative. 1.   f ( x ) = 2 x 10 − 12 x 3 + 4

To determine

To calculate: The second derivative of the function f(x)=2x1018x512x3+4.

Explanation

Given Information:

The function is f(x)=2x1018x512x3+4.

Formula used:

According to the power rule, if f(x)=xn, then,

f(x)=nxn1

According to the property of differentiation, if a function is of the form, g(x)=cf(x), then,

g(x)=cf(x)

According to the property of differentiation, if a function is of the form f(x)=u(x)+v(x), then,

f(x)=u(x)+v(x)

The derivative of a constant value, k, is

ddx(k)=0

Calculation:

Consider the provided function,

f(x)=2x1018x512x3+4

To find the first order derivative, differentiate both sides with respect to x,

f(x)=ddx(2x1018x512x3+4)=ddx(2x10)ddx(18x5)ddx(12x3)+ddx(4)=2ddx(x10)18ddx(x5)12

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