Let f be the function given by , where p is an arbitrary constant.

a) Write an expression for f ' (x) and use it to find therelative maximum and minimum values of f in terms of p. Show theanalysis that leads to your conclusion.

b) For what values of p does f have three distinct realroots?

c) Find the value of p such that the average value of f overthe closed interval [-1,2] is

 

f(x)= x - 6x +p