Find the c value that satisfies the Mean Value Theorem of the function f(x)= x^3-x on the interval [0, 2]. c=

Answer 1

f(x) is differentiable over (0,2) and continuous over [0,2]

f'(x)=3x^2 -1

f(0)=0, f(2)= 6

f'(c)= (6-0)/(2-0)= 6/2= 3= 2(c^2)-1= average rate of change

2c^2 =4

c^2=2

c=sqr2