24. Find the constants a and b such that the function below is continuous at x = 0 and x = 1 1 - x², f(x) = X≤0 ax+b, 0 < x ≤1 (x-1)3 + 2, x > 1

Show that Rolle’s theorem is false for the function f(x) = |x| on the interval [−2, 2]. How can a ”theorem” be true all the time, but false on this example?

5. Use calculus to find the interval(s) on which the function f (x) = x-e increases.