AP

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Let p(x)=(x−3)2−9p(x)=(x-3)^{2}-9. (a) Find p(3−h)p(3-h) and p(3+h)p(3+h), where h≠0h\neq0. (b) Show that the average rate of change of pp from x=3−hx=3-h to x=3+hx=3+h is 00 for every non-zero hh. (c) Explain geometrically why the result in part (b) is expected from the symmetry of the parabola y=p(x)y=p(x).

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