Determine whether the hypotheses of the Mean Value Theorem are satisfied for the…

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Determine whether the hypotheses of the Mean Value Theorem are satisfied for the function

f(x)=x^{3}-6x^{2}+9x

on the interval

[0,3]

. State whether the theorem guarantees a value

c

(0,3)

such that

f'(c)=\dfrac{f(3)-f(0)}{3-0}

. Provide a brief justification.