Please see the file attached.
For suitably "nice" functions, the second derivative can be used to find where the function is concave up and down. The first derivative and second derivative together can be used to find the relative maxima and minima of the function, which can in turn be used to help find any absolute minima or maxima.
Contained is the solution to 5 questions related to these topics, comprising 3 pages written in Word with equations in Mathtype. Each step is fully explained. The inequalities arising in the course of the questions are solved using the split point method (which is also briefly explained)