State the Mean Value theorem including all assumptions. Use it to prove that the function f(x)= (x^5-x+8)sin(xpi), has a critical point somewhere on the interval [0,1].
Feel free to do that. Go ahead. State it.
Then notice that:
f(0)= (0^5-0+8)sin(0(pi)) = 8*0 = 0
f(1)= (1^5-1+8)sin(1(pi)) = 8*0 = 0
That's unusual. Is f(x) a constant function? Maybe we should appeal to ALL the criteria for the Mean Value Theorem.
Note: Please stop posting problems with no work shown. Personally, I weary quickly of such laziness.