Mathematics

Mathematics

Problem

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

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