Calculus Mean Value Theorem Question..!?

Question

This involves the Mean Value Theorem. 

Let [a,b] = [0,1] and let f(x) = x^3. Find a number c= ______ such that 

f(b) -f(a) = f'(c)(b-a).

Answer 1

The given function is f (x) = x³ and the interval is [ a , b ] =[ 0, 1 ].

From mean value theorm ,

Now f (b) =f (1) =  =  1.

f(a) = f(0) =(0) = 0.

Now 

=(1 - 0) / 1= 1.

From mean value theorm =0

Hence the value of  .