Question

If f(x) = ∣(x^2 − 6)(x^2 + 2)∣, how many numbers in the interval 1 ≤ x ≤ 2 satisfy the conclusion of the mean value theorem?
a. none
b. one
c. two
d. three

Answer 1

@Abhisar @Hero @iambatman @Michele_Laino @satellite73 @TheSmartOne @Zale101

Answer 2

please note that within the interval (1,2) x^2-6 is negative

Answer 3

@Michele_Laino what do you mean?

Answer 4

I meant that
\[f(x) = \left( {6 - {x^2}} \right)\left( {{x^2} + 2} \right)\]
when x is in [1,2]

Answer 5

we have to solve this equation:
\[4{x^3} - 8x - 3 = 0\]

Answer 6

oh ok

Answer 7

i got 3 is that right @Michele_Laino