   Chapter 9.4, Problem 45E ### 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

# For each function in Problems 43-46, do the following.(a) Find f'(x).(b) Graph both f(x) and f'(x) using a graphing calculator.(c) Use the graph of f'(x) to identify x-values where f ' ( x ) =   0 ,   f ' ( x ) >   0 ,  and  f ' ( x ) <   0 . (d) Use the graph of f(x) to identify x-values where f(x) has a maximum or minimum point, where the graph of f(x) is rising, and where the graph of f(x) is falling. f ( x ) = x 3 − 12 x − 5

(a)

To determine

To calculate: The derivative of the function f(x)=x312x5.

Explanation

Given Information:

The function, f(x)=x312x5

Formula Used:

According to sum rule of derivatives,

If f(x)=u(x)+v(x) then,

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

According to power rule,

If f(x)=xn, then f(x)=nxn1.

According to constant function rule,

If f(x)=c, then f(x)=0.

Coefficient rule for a constant c is such that, if f(x)=cu(x), where u(x) is a differentiable function of x, then f(x)=cu(x).

Calculation:

The given function is;

f(x)=x312x5

(b)

To determine

To graph: The function f(x)=x312x5 and f(x)=3x212.

(c)

To determine

The value of x from the graph where f(x)=0, f(x)>0 and f(x)<0.

(d)

To determine

The value of x from the graph where f(x) has the maxima or minima and where the graph is falling and rising.

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