Let be a constant and let on the interval

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

Problem

Let

k>0

be a constant and let

f(x)=e^{kx}

on the interval

[0,1]

. Determine, in terms of

k

, the value of

c

(0,1)

at which

f'(c)

equals the average rate of change of

f

over

[0,1]