A differentiable function is concave down on the interval
MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
A differentiable function h is concave down on the interval [2.5,3.5]. Two estimates for h′(3) are obtained:
• Using h(2.9)=5.61 and h(3.1)=5.95
• Using h(2.5)=4.85 and h(3.5)=6.15
(a) Compute each estimate.
(b) Indicate which estimate is likely closer to the actual value of h′(3) and state a brief reason based on the given concavity.