6 -/6 points V My Notes Use Rolle's theorem to show that the function f(x) = 2x - 4x7 cannot take on the same value twice on the interval [1, 20). Assume there are two numbers a and b in [1, ) such that fa) = ((b]. By Rolle's Theorem, there exists at least one ce (a, b) c (1, ce) such that / [c) = 0, but /"[c) = 0 for this function occurs when / [x) = = 0 hence the only critical numbers are at *= -1, x = 0, and x = Since none of these numbers is in (1, co), there is no c E (a, b) such that / (c) = 0, which is a contradiction. Thus fa) cannot equal Ab) for any a, b E [1, so), or in other words, the function cannot take on the same value twice in this interval. 7 0/6 points V Previous Answers My Notes Show that the function f(x] = - x2+4 - has an absolute maximum but not an absolute minimum. f(x) = - -'. Verify the mean value theorem by finding a CE (-2, 1) such that fTe) = 1) - 1(-2) 1 - (-2)