(a)
The function .
Find the intercept:
Consider .
Find the intercept, by substituting in .
.
The intercept is .
(b)
Find for what numbers the graph of is decreasing in the interval is .
The function .
Apply derivative on each side 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 , .
If ,
The solutions are , and in the interval .
The critical points are , and and the test intervals are .
Interval  Test Value  Sign of  Conclusion 

Increasing  

Decreasing 
The function is Decreasing over the interval .
(c)
The function and the interval is .
The critical points are and and .
Find the values of at these critical points.
.
.
.
Compare the values of to find the absolute minimum.
Absolute minimum 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 , .
The solutions are , and in the interval .
General solution of is , where is an integer.
General solution: .
If , .
If , .
The solutions are and in the interval .
(f)
General solution of is , where is an integer.
General solution: .
If , .
If , .
If , .
The solutions are 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 Decreasing over the interval .
(c). Absolute minimum 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 in the interval .
(g).The intercepts are , where is an integer.
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