Answer the following questions about the relationship between the degree of a…
MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
Answer the following questions about the relationship between the degree of a polynomial and the degree of its derivative.
(i) Explain, without carrying out explicit differentiation, why the derivative of a non-constant polynomial of degree n must be a polynomial of degree n−1.
(ii) Using your reasoning from part (i), predict the degree of the derivative of q(x)=7x9−5x4+3.
(iii) Verify your prediction in part (ii) by differentiating q(x) and writing the resulting polynomial.