Subject: Rolle's Theorem - Calculus
Who are you: Student
If f(x) = (x^2)(square root of [3-x]) on the interval [0,3] is given,
Does Rolle's Theorem apply? If yes, find any values of c such that f '(c)=0
For Rolle's Theorem to apply the function f(x) must be continuous for x in [0,3] and f(x) must be differentiable for x in (0,3). The function f(x) is only a problem if you attempt to take the square root of a number, that is if x > 3, hence f(x) satisfies the conditions of Rolle's theorem.
To find a number c such that c is in (0,3) and f '(c) = 0 differentiate f(x) to find f '(x) and then solve f '(c) = 0. Some of the solutions to this equations may not lie in (0,3) so make sure you find one that does.