A differentiable function satisfies ,

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

A differentiable function qq satisfies q(0.98)=2.45q(0.98)=2.45, q(1)=2.51q(1)=2.51, and q(1.02)=2.57q(1.02)=2.57. Two students estimate q′(1)q'(1). • Student A uses q(1.02)−q(1)0.02\dfrac{q(1.02)-q(1)}{0.02}. • Student B uses q(1.02)−q(0.98)0.04\dfrac{q(1.02)-q(0.98)}{0.04}. Identify which student’s estimate is expected to be closer to the true value of q′(1)q'(1) and state that estimate.

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