Chapter 11.3, Problem 76E

a.

To determine

To match: the given function with the graph of its derivatives.

Answer to Problem 76E

The graph of the derivative of f(x) is graph (ii).

Explanation of Solution

Given information: Given function is $f(x)=\sqrt{x}$ . The graphs are shown below.

  

Calculation:

The graph of the given function $f(x)=\sqrt{x}$ using graphing utility is shown below.

  

f’(x) gives the rate of change of the function f(x) at a given value of x . When f’(x) < 0, the function is decreasing; the function is increasing when f’(x) > 0. The magnitude of f’(x) describe how quickly the graph of f(x) is changing.

From the graph of the function f(x), the graph of the derivative of f(x) is graph (ii).

b.

To determine

To match: the given function with the graph of its derivatives.

Answer to Problem 76E

The graph of the derivative of f(x) is graph (i).

Explanation of Solution

Given information: Given function is $f(x)=\frac{1}{x}.$ .

Calculation:

The graph of the given function $f(x)=\frac{1}{x}.$ using graphing utility is shown below.

  

f’(x) gives the rate of change of the function f(x) at a given value of x . When f’(x) < 0, the function is decreasing; the function is increasing when f’(x) > 0. The magnitude of f’(x) describe how quickly the graph of f(x) is changing.

From the graph of the function f(x), the graph of the derivative of f(x) is graph (i).

c.

To determine

To match: the given function with the graph of its derivatives.

Answer to Problem 76E

The graph of the derivative of f(x) is graph (iv).

Explanation of Solution

Given information: Given function is $f(x)=x.$ .

Calculation:

The graph of the given function $f(x)=x.$ using graphing utility is shown below.

  

f’(x) gives the rate of change of the function f(x) at a given value of x . When f’(x) < 0, the function is decreasing; the function is increasing when f’(x) > 0. The magnitude of f’(x) describe how quickly the graph of f(x) is changing.

From the graph of the function f(x), the graph of the derivative of f(x) is graph (iv).

d.

To determine

To match: the given function with the graph of its derivatives.

Answer to Problem 76E

The graph of the derivative of f(x) is graph (iii).

Explanation of Solution

Given information: Given function is $f(x)=x^3$ .

Calculation:

The graph of the given function $f(x)=x^3$ using graphing utility is shown below.

  

f’(x) gives the rate of change of the function f(x) at a given value of x . When f’(x) < 0, the function is decreasing; the function is increasing when f’(x) > 0. The magnitude of f’(x) describe how quickly the graph of f(x) is changing.

From the graph of the function f(x), the graph of the derivative of f(x) is graph (iii).