MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
Let f(x)=x3−6x2+9x+7.
(a) Find the expression for the average rate of change of f between x=a and x=a+h, where h=0.
(b) Simplify the expression obtained in part (a) so that it is written as a polynomial in a and h.
(c) Using the simplified expression, calculate the average rate of change of f between x=2 and x=5.
(d) For x=2, determine the value of h(h=0) for which the average rate of change of f between x=2 and x=2+h equals −3.