Intermediate Value Theorem (IVT)

Let $f$ be a continuous function such that $f'$ is also continuous. Suppose $f(a) = 2$ and $f(b) = 4$ for $a < b$. Also suppose that $f'(a) = 3$ and $f'(b) = 5$.

True or false: There must exist $c \in (a,b)$ such that $f(c) = 3$ and $f'(c) = 4$.