MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
Consider the polynomial function p(x)=3x4−5x2+7.
(a) Describe, without performing explicit calculations, how the structure of p(x) guarantees that its derivative can be obtained by differentiating each term separately.
(b) Explain why the constant term in p(x) does not contribute to the derivative.
(c) Without computing p′(x) explicitly, state the degree of p′(x) and justify your answer based on the properties of polynomial differentiation.