The Intermediate Value Theorem has been proved already: a continuous function on an interval $[a,b]$ attains all values between $f(a)$ and $f(b)$. Now I have this problem:
Verify the Intermediate Value Theorem if $f(x) = \sqrt{x+1}$ in the interval is $[8,35]$.
I know that the given function is continuous throughout that interval. But, mathematically, I do not know how to verify the theorem. What should be done here?