Question

Suppose f(x) = x^3 on the interval [1, 4]. Use the Mean Value Theorem to find all values c in the open interval (1, 4) such that f'(c)= (f(4)-f(1))/4-1

c= square root of 7
c= cubed root of 21
c = 7
Mean Value Theorem does not apply

Answer 1

f(4) = 64
f(1) = 1
63/3 = 21 = average slope in interval

f' = 3 x^2 = 21
x = +/- sqrt 7
in interval
x = sqrt 7 = c
so A