Values of a differentiable function are recorded every units of at ,

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

Problem

Values of a differentiable function gg are recorded every 0.20.2 units of xx at x=a−0.2x=a-0.2, x=ax=a, and x=a+0.2x=a+0.2. Which of the following estimation schemes is most likely to yield the smallest truncation error when approximating g′(a)g'(a)? (a) g(a+0.2)−g(a−0.2)0.2\dfrac{g(a+0.2)-g(a-0.2)}{0.2} (b) g(a+0.2)−g(a−0.2)0.4\dfrac{g(a+0.2)-g(a-0.2)}{0.4} (c) g(a+0.2)−2g(a)+g(a−0.2)0.2\dfrac{g(a+0.2)-2g(a)+g(a-0.2)}{0.2} (d) g(a+0.2)−g(a)0.2\dfrac{g(a+0.2)-g(a)}{0.2}

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