Verify Mean Value Theorem: f(x)=3x^2+6x+7 on [-2,3]

[Rasine]

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?

 

[Dick]

You seem to have computed 45-30=5?!

 

[Rasine]

oohhh my! thank you so much! i didnt see that !