Step 1:

The function is and points and .

The Q points are :

Step 2 : 

Find the secant line passing through the points and .

Let and .

Slope intercept form of the line equation where  m is slope and b is y-intercept.

The line equation PQ is

Find the y- intercept by substituting any point on line PQ , say .

The line equation PQ is .

Step 3: 

Find the secant line passing through the points and .

Let and .

Slope intercept form of the line equation where  m is slope and b is y-intercept.

The line equation PQ is

Find the y- intercept by substituting any point on line PQ , say .

The line equation PQ is .

Step 4: 

Find the secant line passing through the points and .

Let and .

Slope intercept form of the line equation where  m is slope and b is y-intercept.

The line equation PQ is

Find the y- intercept by substituting any point on line PQ , say .

The line equation PQ is .

The secant lines are , , and .

Step 5:

The graph of the function and the secant lines is :

Step 6:

(b)

The secant lines are , , and .

The slopes of the secant lines are .

Step 7:

(c)

The function is

Differentiate the function with respect to x

The slope of the tangent line at point

.

This is the slope of the tangent line.

Solution :

 (a)

The graph of the function and the secant lines is :

(b)

The slopes of the secant lines are .

(c)

The slope of the tangent line is .