MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
The function h is differentiable, and its tangent line at x=4 is used to estimate nearby values. The tangent-line formula gives htan(4.05)=7.26, while the actual value is h(4.05)=7.31. Which of the following statements about h′′(4) is most consistent with this information?
(a) h′′(4)>0 because the tangent-line estimate is an overestimate.
(b) h′′(4)<0 because the tangent-line estimate is an underestimate.
(c) h′′(4)>0 because the tangent-line estimate is an underestimate.
(d) h′′(4)=0 because the estimate and actual value differ by only 0.05.