The graph of a differentiable function passes through the point

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

The graph of a differentiable function y=f(x)y=f(x) passes through the point (3,2)(3,2). A line that appears tangent to the curve at x=3x=3 also passes through the point (5,5)(5,5). Which is the best estimate of f′(3)f'(3)? (a) 2.52.5 (b) 1.51.5 (c) 23 (≈0.667)\dfrac{2}{3}\,(\approx 0.667) (d) 3.03.0

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