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: 

The straight-line distance between the parents' and grandparents' houses = 9.83 miles.

Step-by-step explanation:

Given - To get to his parents' house, Mateo would have to drive due north 2.1 miles. To get to his grandparents' house, he would have to drive due east 9.6 miles.

To find - What is the straight-line distance between the parents' and grandparents' houses? If necessary, round to the nearest tenth.

Solution -

By the given information, the figure becomes -

From the Graph, we can see that,

The side MP = 2.1

The side MG = 9.6

And By using Pythagoreas Theorem, we get

(PG)² = (MG)² + (MP)²

⇒(PG)² = (9.6)² + (2.1)²

⇒(PG)² = 92.16 + 4.41

⇒(PG)² = 96.57

⇒PG = √96.57

⇒PG = 9.827

∴ we get

The straight-line distance between the parents' and grandparents' houses = 9.83 miles.