Please answer the question and provide proper explanation. Please make sure that the answer is visible and easy to see.

4) Determine whether each of the following statements about functions is always true or sometimes false. If it is always true, explain why. If it is sometimes false, provide an example of a function for which it is false. (@) If f'(a) = 0, then f(x) has a local maximum or minimum at x = a. [If you think it's false: find a function where f '(@) = 0 and f(x) doesn't have a local maximum or minimum at x = a.] (b) If a function f(x) has a global maximum at x = a, thenx = a is a critical number for x. [If you think it's false: find a function with a global maximum at some number a, but which doesn't have a critical number at x = a. ] (c) If a function f(x) is concave up at a point x = a, then f '(a) > 0. [If you think it's false: find a function that is concave up at some point x = @, but has a negative first derivative at that point.]