#### To determine

**To find:** The slope of the graph at the origin.

#### Answer

The slope at origin appears to be 1.

#### Explanation

**Graph:**

Use the online graphic calculator and draw the graph as shown in Figure 1.

From the graph, it is observed that at the origin, the slope appears to be 1.

#### To determine

**To estimate:** The value of f′(0) and does it agree with the answer from part (a).

#### Answer

The value of f′(0) is 1.

#### Explanation

**Result used:**

The slope of the line passing through the points (x1,y1) and (x2,y2) is y2−y1x2−x1.

**Graph:**

Use the online graphic calculator and draw the graph as shown in Figure 2.

Obtain the values f′(0).

From the given graph, draw the tangent line at x=0 is approximately joining the points (0,0) and (0.1,0.1).

Use the slope formula stated above and compute the slope of the line passing through the points (0,0) and (0.1,0.1).

f′(0)=0.1−00.1−0=0.10.1=1

Therefore, the value of f′(0) is 1.

From part (a), at origin point the slope appears to be 1.

Therefore, the slope of the function f(0) is 1 and it is same as the result in part (a).

#### To determine

**To revise:** The estimate for f′(0).

#### Explanation

**Graph:**

Use the online graphic calculator and draw the graph as shown in Figure 3.

From Figure 3, it is observed that the estimate is true.

Then, the slope of the function f(0) appears to be zero.