Mean Value Theorem for |(x^2 - 12)(x^2 + 4)| on [-2, 3]

[Math wiz ya rite 09]

If f(x) = | (x^2 - 12)(x^2 + 4) |, how many numbers in the interval -2 <= x <= 3 satisfy the conclusion of the Mean Value Theorem?

A. None
B. One
C. Two
D. Three
E. Four

 

[Deleted member 4993]

Re: mean value theorem

If f(x) = |(x^2-12)(x^2+4)|, how many numbers in the interval -2 <= x <= 3 satisfy the conclusion of the Mean Value Theorem?

A. None
B. One
C. Two
D. Three
E. Four

Before attacking the problem theoretically - plot the curve approximately. I am saying approximately because ranging the curve in the calculator might be difficult.

Now plot the function without the "absolute" value.

Now observe the difference and decide what would be the answer. Then justify theoretically.