Question

If f(x) = |(x2 - 10)(x2 + 1)|, how many numbers in the interval 0 ≤ x ≤ 2.5 satisfy the conclusion of the mean value theorem?

Answer 1

x^2+1>0 for all x
f(x)=(x^2+1)|x^2-10|

y=x^2-10 looks like
so y=|x^2-10| looks like that except with the middle part reflected about the x-axis
that is |x^2-10| actually equals -(x^2-10) on the interval -sqrt(10) to sqrt(10)