A function is defined by p(x)=x7−4x5 for all real x.
(a) Calculate the third derivative p′′′(x). Show all intermediate steps.
(b) Evaluate p′′′(2).
(c) Describe what the sign of p′′′(2) indicates about the rate of change of concavity of p at x=2. Justify your answer using appropriate calculus terminology.