I need help with the last part of this question. I know the function is continuous everywhere because it is a polynomial function, I set the derivative equal to zero and I got a critcal number at 1/3. But it says that answer for the critical number is wrong so I do not know what the others are or what I did wrong. Please help

4. [3.33/6.66 Points] DETAILS PREVIOUS ANSWERS SESSCALC2 3.2.009. Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = 3x2 - 2x + 1, [0, 2] Yes, it does not matter if f is continuous or differentiable, every function satifies the Mean Value Theorem. Yes, f is continuous on [0, 2] and differentiable on (0, 2) since polynomials are continuous and differentiable on R. O No, f is not continuous on [0, 2]. O No, f is continuous on [0, 2] but not differentiable on (0, 2). There is not enough information to verify if this function satifies the Mean Value Theorem. If it satisfies the hypotheses, find all numbers c that satisfy the conclusion of the Mean Value Theorem. (Enter your answers as a comma-sepa DNE). Viewing Saved Work Revert to Last Response Submit Answer 5. [6.66/6.66 Points] DETAILS PREVIOUS ANSWERS SESSCALC2 3.3.001.MI. 65,401 OCT 10 MacBook Pro I'm We 9 3 15 N W E R T U D G H S