Chapter 9.4, Problem 46E

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Chapter
Section

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
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 ,   a n d   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 ) = 7 − 3 x 2 − x 3 3

(a)

To determine

To calculate: The derivative of the function f(x)=73x2x33.

Explanation

Given Information:

The function, f(x)=7âˆ’3x2âˆ’x33

Formula Used:

According to sum rule of derivatives,

If

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

Then,

fâ€²(x)=uâ€²(x)+vâ€²(x)

According to power rule,

If f(x)=xn, then fâ€²(x)=nxnâˆ’1.

According to constant function rule,

If f(x)=c, then fâ€²(x)=0.

Coefficient rule for a constant c is such that, if f(x)=câ‹…u(x), where u(x) is a differentiable function of x, then fâ€²(x)=câ‹…uâ€²(x)

(b)

To determine

To graph: The function f(x)=73x2x33 and f(x)=6xx2

(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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