A twice-differentiable function satisfies for all in the interval

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

Problem

A twice-differentiable function mm satisfies ∣m′′(t)∣≤0.6|m''(t)|\le 0.6 for all tt in the interval [3,3.1][3,3.1]. An estimate of m′(3)m'(3) is formed with the quotient m(3.1)−m(3)0.1\dfrac{m(3.1)-m(3)}{0.1}. Determine a numerical upper bound for the absolute error of this estimate.

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