The differentiable function is defined for all real numbers

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

Problem

The differentiable function gg is defined for all real numbers, and g′(5)g'(5) exists. Which of the following difference quotients is most likely to give the best numerical approximation of g′(5)g'(5)? (a) g(5.1)−g(4.9)0.2\dfrac{g(5.1)-g(4.9)}{0.2} (b) g(5.001)−g(5)0.001\dfrac{g(5.001)-g(5)}{0.001} (c) g(6)−g(5)1\dfrac{g(6)-g(5)}{1} (d) g(5)−g(4)1\dfrac{g(5)-g(4)}{1}

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