Step 1 :

 (a)

Find the y - intercept :

The function .

Let the function

Find the y - intercept, by substituting in .

.

The y - intercept is zero.

Step 2 :

(b)

The function and the interval is .

Differentiate the function with respect to :

Determination of critical points :

The critical points exist when .

Equate to zero:

Solve in the interval .

General solution of is , where is an integer.

General solution is

If , .

If , .

The solutions are in the interval .

The critical points are and the test intervals are .

Interval	Test Value	Sign of	Conclusion
		\ \	Decreasing
		\ \	Increasing
		\ \	Decreasing

The function is increasing over the interval .

Step 3 :

(c)

The function and the interval is .

The critical points are .

Find the values of at these critical points.

.

.

Find the values of at the end points of the interval.

.

.

Compare the four values of to find the absolute maximum.

Absolute maximum value is .

Step 4 :

(d)

The function and the interval is .

General solution of is , where is an integer.

General solution : .

If , .

If , .

If , .

The solutions are in the interval .

Step 5 :

(e)

The function and the interval is .

General solution of is , where is an integer.

General solution : .

If , .

If , .

If , .

The solution is in the interval .

General solution of is , where is an integer.

General solution : .

If , .

If , .

If , .

If , .

The solution is in the interval .

Step 6 :

(f)

General solution of is , where is an integer.

General solution : .

If , .

If , .

If , .

If , .

The solution is in the interval .

Step 7 :

(g)

 Find the x - intercept :

The function .

Let the function .

Find the x - intercept, by substituting in .

General solution of is , where is an integer.

General solution is , where is an integer.

The x - intercept are , where is an integer.