For on the interval

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

For

f(x)=\ln x

on the interval

[1,e^{2}]

, the average rate of change is

\dfrac{2}{e^{2}-1}

. At which value of

x

(1,e^{2})

does the instantaneous rate of change equal this average? (a)

\dfrac{e^{2}}{2}

(b)

\dfrac{1+e^{2}}{2}

(c)

\dfrac{e^{2}-1}{2}

(d)

e