Consider the function on the interval

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

Problem

Consider the function

f(x)=e^{2x}

on the interval

[0,1]

. (a) Prove that there is exactly one

c\in(0,1)

for which

f'(c)

equals the average rate of change of

f

[0,1]

. (b) Calculate this value of

c

correct to four decimal places.