Now, the function is increasing if the slope is positive and vice versa.
For all .
I hope you can solve the rest of the problem from this:
the local minima and maxima are situated at the critical points.
if the second derivative is positive, the graph is convex. if it is negative, it is concave.
the point of inflection is where the second derivative changes signs (ie. from +ve to -ve or vice versa). therefore, it becomes zero.
Thanks to defunkt for pointing this out. 9pi/4 is obviously > 2pi. Read all occurrences as 5pi/4. (can't believe I was stupid enough to miss it)