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?

none

one

two

three

  Two

Step-by-step explanation:

The mean value theorem tells you that a continuous, differentiable function will have at least one point between the endpoints of any interval where the slope of the function is equal to the average slope on the interval.

Here, f(x) is both continuous and differentiable on [0, 2.5], so the conclusion is guaranteed for at least one point. In the given interval, the curve f(x) crosses the line of average slope so has two points where a tangent has the average slope.

There are two values of x in the interval that satisfy the conclusion of the mean value theorem.

the expected value of the random variable : 0, 1 and 2

step-by-step explanation: