1. Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.)
f(x) = x3 -x2 - 12x + 3, [0, 4]
2. Show that the equation has exactly one real root.
x + cos x = 0.
3. Suppose that for 4 ≤ f'(x) ≤ 5 for all values of x. What are the minimum and maximum possible values of f(6) - f(1)?
4. Find the absolute maximum and absolute minimum values of f on the given interval.
f(x) = xe-e^2/32, [-2, 8]
5. Find the critical points of the function. (Enter your answers as a comma-separated list.)
g(x) = √(1 - x2)