Don't really know how to prove this at all, I'm much appreciative of any help, i posted this once before, but really need more of an intro way to solve this proof.
Let f : [a,b] ⇒ ℝ be a continuous function. Show that there exists a w in [a,b] such that
a
∫ f(t)dt = f(w)(b-a)
b
Here is the hint that i need to use to solve this problem:
f attains a smallest value A and a largest value B. Show that:
-----------a-----------------------------------------
A ≤ 1/(b-a)∫ f(t)dt ≤ B
-----------b-----------------------------------------
Thank you again for the help!