Let on the interval

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

Problem

Let

f(x)=e^{2x}+x

on the interval

[0,1]

. Which value of

c

(0,1)

makes the instantaneous rate of change of

f

equal its average rate of change on the interval? (a)

\ln\!\left(\dfrac{e^{2}-1}{2}\right)

(b)

\dfrac{1}{2}\,\ln\!\left(\dfrac{e^{2}+1}{2}\right)

(c)

\dfrac{1}{2}\,\ln\!\left(\dfrac{e^{2}-1}{2}\right)

(d)

\dfrac{1}{2}\,\ln\!\left(\dfrac{e^{2}}{2}\right)