#### To determine

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

#### Answer

The value of f′(0) is 6.7.

#### Explanation

**Estimation**:

Draw the tangent at x=0

The calculation of the slope at x=0 is as follows,

From Figure 1,

m=2−00.3−0=20.3=6.67

Thus, f′(0)=6.67

#### To determine

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

#### Answer

The value of f′(1) is 0.

#### Explanation

**Estimation:**

Draw the tangent at x=1

From the Figure 2, it is clear that the tangent to the graph at x=1 is horizontal. So, f′(1)≈0.

Thus, f′(1)=0.

#### To determine

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

#### Answer

The value of f′(2) is −1.5

#### Explanation

**Estimation:**

Draw the tangent at x=2

**Calculation:**

The calculation of the slope of *f* at x=2 as follows,

From Figure 3,

m=0−1.53−2=−1.51=−1.5

So, f′(2)≈−1.5

Thus, f′(2)=−1.5.

#### To determine

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

#### Answer

The value of f′(3) is −1

#### Explanation

**Estimation:**

Draw the tangent at x=3

From Figure 4, the estimation of the slope of *f* at x=3 as follows,

m=−1−14−2=−22=−1

So, f′(3)≈−1

Thus, f′(3)=−1.

#### To determine

**To estimate:** The value of f′(4) using the graph of *f.*

#### Answer

The value of f′(4) is −1.

#### Explanation

**Estimation:**

Draw the tangent at x=4

From Figure 5, the calculation of the slope of *f* at x=4 as follows,

m=−2−05−3=−22=−1

So, f′(4)≈−1

Thus, f′(4)=−1.

#### To determine

**To estimate:** The value of f′(5) using the graph of *f.*

#### Answer

The value of f′(5) is −0.2

#### Explanation

**Estimation:**

Draw the tangent at x=5

From Figure 7, the calculation of the slope of *f* at x=5 as follows,

m=−1.8+1.46−4=−0.42=−0.2

So, f′(5)≈−0.2

Thus, f′(5)=−0.2.

#### To determine

**To estimate:** The value of f′(6) using the graph of *f.*

#### Answer

The value of f′(6) is 0.

#### Explanation

**Estimation**:

Draw the tangent at x=6

From the Figure 7, it is clear that the tangent to the graph at x=6 is horizontal. So,f′(6)≈0.

Thus, f′(6)=0.

#### To determine

**To estimate:** The value of f′(7) using the graph of *f.*

#### Answer

**Solution**:

The value of f′(7) is 0.15.

#### Explanation

**Estimation**:

Draw the tangent at x=7

The calculation of the slope of the graph at x=7 is as follows,

From the Figure 8,

m=−1.6+1.98−6=0.32=0.15

So,f′(7)≈0.15

Thus, f′(7)=0.15

To sketch the graph of f′ use the information from all the above parts to draw the graph of f′(x)

From Figure 9, it is observed that the graph of f′ is positive on the interval (0,1)∪(6,7) and negative in (1,6).