Question

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

Yes, x equals one half.
Yes, x equals 4 over 3.
Yes, x equals 25 over 9.
No, the theorem does not apply.

I put b and got it wrong

Answer 1

The theorem does not apply.

1. Set the function f(x)=sqrt(x-1) equal to 0 to find what values of x make f(x) defined. So:

x - 1 is < or = to 0

x > or = to 0

2.) find the values where x is defined:

x - 1 > or = to 0

x > or = to 0

Domain = all values of x that define f(x)

[1,infinity)

{x|x> or = to 1}

DNE because 1 is not in the domain because (1-1)^1/2 = 0.