(a)
The function .
Find the intercept:
Find the intercept, by substituting in .
.
The intercept is .
(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 .
(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 .
(d)
The function and the interval is .
General solution of is , where is an integer.
General solution: .
If , .
If , .
If , .
The solutions are and in the interval .
(e)
The function and the interval is .
General solution of is , where is an integer.
General solution: .
If , .
If , .
If , .
If , .
The solution is and in the interval .
General solution of is , where is an integer.
General solution: .
If , .
If , .
If , .
If , .
The solution is and in the interval .
(f)
General solution of is , where is an integer.
General solution: .
If , .
If , .
If , .
If , .
If , .
If , .
The solutions are and in the interval .
(g)
Find the intercept:
The function .
Find the intercept, by substituting in .
General solution of is , where is an integer.
The intercepts are , where is an integer.
(a). The intercept is .
(b).The function is increasing over the interval .
(c). Absolute maximum value is .
(d).The solutions are and in the interval .
(e). For , the solutions are and in the interval .
For , the solutions are and in the interval .
(f). The solutions are and in the interval .
(g).The  intercepts are , where is an integer.
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