please explain. thank you

4. (4 points) Given that f'(a) is continuous everywhere and the y-values of f'(x) change from positive to negative at a = a. which of the following statements must be true? Select ALL that that are TRUE. (Write the letter(s) corresponding to your selection(s) in the box below.) (a) a is a critical point of f(x). (b) f(a) is a local minimum of f. (c) f(a) is a local maximum of f. (d) f'(a) is a local minimum of f. (c) S'(a) is a local maximum of S'. a,b,d,c 5. (4 points) On the axis below, sketch the graph of a function, f, which has a critical point at a but for which S'(1) # 0. 5 -5