Determine whether the Mean Value theorem can be applied to f on the closed interval

Question

f(x) = 4x³,    [1, 2]

I got √7/3 is this correct?

Answer 1

Hi Celine,

f(x) = 4x³,    [1, 2]

First, find the slope at x = 1 . x = 2

how do you find the slope ? slope = ( f(1) - f(2) ) / (1 - 2)

f(1) = 4(1)³ = 4 and f(2) = 4 (2 )³ = 32 slope = ( 4 - 32 ) / ( 1 - 2) = 28

Second , find derivative of given function f'(x) = 12 x²

Third, f'(c ) =12 c² = slope = 28 c = √ 7/3 and your answer is correct.

I hope it is useful,

Minoo

Answer 2

Yes, MVT can be applied because the function is continuous on the closed interval and differentiable on the open. As long as your √ Included the entire ratio √(7/3), it was correct. Or √21/3 if rationalized.