x f(x) f'(x) g(x) g'(x)

1 6 4 2 5

2 9 2 3 1

3 10 -4 4 2

4 -1 3 6 7

The functions f & g are differentiable for all reals and g is increasing.

A) Explain why there MUST be a value r for such that

b) Explain why c for such that

I don't get how the value theorems tie into this problem.