Urgent! Please help solve Given f(x)=x^3 use the Mean Value Theorem and find all point c , 0

Question

Urgent! Please help solve Given f(x)=x^3 use the Mean Value Theorem and find all point c , 0<c<2 , such that f(2)−f(0)=f′(c)(2−0)?

fcas80 · Answer

f(x)=x^3,    f ' (x)=3x^2

There is a c so that 3c^2 = (2^3 - 0^3)/(2-0) = 4

3c^2 = 4
c = (4/3)^(1/2)

Urgent! Please help solve Given f(x)=x^3 use the Mean Value Theorem and find all point c , 0<c<2 , such that f(2)−f(0)=f′(c)(2−0)?