A function is defined by for all real .

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

A function is defined by p(x)=x7−4x5p(x)=x^{7}-4x^{5} for all real xx. (a) Calculate the third derivative p′′′(x)p'''(x). Show all intermediate steps. (b) Evaluate p′′′(2)p'''(2). (c) Describe what the sign of p′′′(2)p'''(2) indicates about the rate of change of concavity of pp at x=2x=2. Justify your answer using appropriate calculus terminology.

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