A function is differentiable on an open interval containing
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
A function h is differentiable on an open interval containing x=1. You are told that the tangent-line approximation at x=1 gives h(1.2)≈4.35, while the exact value is h(1.2)=4.21.
(a) Decide whether h′′(1) is positive, negative, or cannot be determined from the information given. Provide a clear explanation.
(b) Assuming that h′′ is continuous at x=1, estimate the sign of h′′(1.2) and justify your answer.