# To estimate: The value of f ′ ( − 3 ) using the graph of f.

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 2.7, Problem 1E

(a)

To determine

## To estimate: The value of f′(−3) using the graph of f.

Expert Solution

The value of f(3) is 0.2.

### Explanation of Solution

Estimation:

Draw the slope of the tangent at the point x=3.

The calculation of the slope at x=3 is as follows,

From the Figure 1,

m=1.9+1.73+4=0.2

Thus, f(3)=0.2.

(b)

To determine

### To estimate: The value of f′(−2) using the graph of f.

Expert Solution

The value of f(2) is 0.

### Explanation of Solution

Estimation:

Draw the slope of the tangent at the point x=2.

From the Figure 2, tt is clear that the tangent to the graph at x=2 is horizontal.

Thus, f(2)=0

(c)

To determine

### To estimate: The value of f′(−1) using the graph of f.

Expert Solution

The value of f(1) is 1.

### Explanation of Solution

Estimation:

Draw the slope of the tangent at the point x=1.

From the Figure 3, Slope of AB

m=1+20.5+1.5=1

Thus, f(1)=1.

(d)

To determine

### To estimate: The value of f′(0) using the graph of f.

Expert Solution

The value of f(0) is 2.

### Explanation of Solution

Estimation:

Draw the slope of the tangent at the point x=0.

From the Figure 4, Slope of AB

m=110.51.5=2

Thus, f(0)=2.

(e)

To determine

### To estimate: The value of f′(1) using the graph of f.

Expert Solution

The value of f(1) is 1.

### Explanation of Solution

Estimation:

Draw the slope of the tangent at the point x=1.

From the Figure 5, Slope of AB

m=211.50.5=1

Thus, f(1)=1.

(f)

To determine

### To estimate: The value of f′(2) using the graph of f.

Expert Solution

The value of f(2) is 0.

### Explanation of Solution

Estimation:

Draw the slope of the tangent at the point x=2.

From the Figure 6, it is clear that the tangent to the graph at x=2 is horizontal.

Thus, f(2)=0.

(g)

To determine

### To estimate: The value of f′(3) using the graph of f.

Expert Solution

The value of f(3) is 0.2.

### Explanation of Solution

Estimation:

Draw the slope of the tangent at the point x=3.

From the Figure 7, Slope of AB

m=1.6242=0.2

Thus, f(3)=0.2.

To Sketch the graph of f, use the information from above parts to draw the graph of f(x) as shown in Figure 8

From Figure 1, it is observed that the graph of f(x) is an even function.

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