1. Please answer all questions fully showing all steps and working leading up to the final answers, thank you

1) In this problem we are given the graph of four functions fi, f2, f3, fs. All of the functions, with one exception, are a derivative of another function in the list. Our task is to identify which is which. An answer could look like fa= fa, f3 = f3, f = f1,and fi is not the derivative of another function in the list; however this is not the answer. The figure is best viewed in colour. You must say how you have reached your conclusion. 4 2 [ | [ LT b S B T I~ z f(1, x _t P _ 3 f2, x ! f(3, x i | I t L r [ L x 2) Recall that in class we showed that if f is differentiable on (a, b) then f is concave up on (a,b) if and only if f'is increasing on (a, b). Suppose that f is concave up on (a,b). Show that f has at most one local minimum on (a,b). 3) Use mathematical induction to prove that 2 1 1P 2?88 e is o i =