**Please do not use integrals.**

F is a differentiable function with a domain of -5.5≤x≤3.5. The graph of f' is the graph above. The graph f' has horizontal tangents at x=-3,-1,1.

1) Find the average rate of change f' on the interval -3≤x≤1

2) Does there have to be a value, k, that exists for -3<k<1 such that f''(k) is equal to the average rate of change from question 1? Show all work.

3) Let h(x)=ln(x)cos(f(x)). It's known that f(-3)=8 so find the value of h'(-3).

4) Find the x-coordinate of each critical point of f on the interval-5.5<x<3.5. Show all work.

5) Identify all critical points from question 4 as a relative minimum, relative maximum, or neither for f. Show all work.

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