Calculus help please

Question

 

Determine if the Mean Value Theorem for Integrals applies to the function  on the interval [1, 5]. If so, find the x-coordinates of the point(s) guaranteed to exist by the theorem. (2 points)

	Yes,  .
	Yes,  .
	Yes,  .
	No, the theorem does not apply.

Answer 1

None of the answers are correct.

Yes, the MVT applies to the function on the interval [1 , 5] since the square root function is continuous on the closed interval and differentiable on the open interval.

f(5) = 2 and f(1) = 0 so the average rate of change is 1/2.

However, the instantaneous rate of change = 1/2 when x = 2, which is the x-value in that interval guaranteed by the MVT.

You can calculate this by finding f’(x), setting it = 1/2, and solving. f’(x) = 1 / √x-1