For the function on the interval

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

For the function f(x)=x2+3xf(x)=x^{2}+3x on the interval [1,4][1,4], find the value of c∈(1,4)c\in(1,4) such that f′(c)f'(c) equals the average rate of change of ff over [1,4][1,4].

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