## Value Theorems

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

$h(x) = f(g(x))-6$

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

A) Explain why there MUST be a value r for $1 < r < 3$ such that $h(r) = -5
$

b) Explain why c for $1 < c < 3$ such that $h'(c) = -5$

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