Determine if the mean value theorem for integrals applies to the function f(x) = 5 − x2 on the interval the closed interval from 0 to the square root of 5. if so, find the x-coordinates of the point(s) guaranteed by the theorem. no, the mean value theorem for integrals does not apply yes, x equals 10 thirds yes, x equals the quotient of square root of 5 and 3 yes, x equals the quotient of the square root of 15 and 3

The mean value theorem for integrals applies as long as the function is continuous and the interval is closed.

The theorem states that there is a y value that is the average of the integral over the interval.

The average of the integral is: 

So, there is a point f(x) = 10/3.

To find x, we substitute that into the original function:







The answer is C. "Yes, x equals the quotient of square root of 5 and 3"

Edit:

The average of an integral of f(x) from a to b is: