MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
The function k is differentiable, and its exact derivative at x=2 is k′(2)=7.389. Limited data are recorded to three decimal places: k(1.99)=7.313 and k(2.01)=7.466.
(1) Using only these data, approximate k′(2).
(2) Compute the percentage error of your approximation, rounded to two decimal places.