# Mean value theorem

Verify that the function satisfies the hypotheses of the Mean Value Theorem on the given interval. Then find all numbers that satisfy the conclusion of the Mean Value Theorem.

f(x)=3x^2+6x+7 on [-2,3]

so f(3)-f(-2)=f'(x)(3+2)

i get 52-7=(6x+6)(5)

then 45=30x+30

then 5=30x

and x=1/6

where am i going wrong?