Suppose that $f(t)$ is continuous and twice-differentiable for $t\ge 0$. Further suppose $f''(t) \ge 3$ for all $t\ge 0$ and $f(0) = f'(0) = 0$.

Using the Racetrack Principle, what linear function $g(t)$ can we prove is less than $f'(t)$ (for $t\ge 0$)?
$g(t) =$

Then, also using the Racetrack Principle, what quadratic function $h(t)$ can we prove is less than than $f(t)$ (for $t\ge 0$)?
$h(t) =$

For both parts of this problem, be sure you can clearly state how the theorem is applied to prove the indicated inequalities.

You can earn partial credit on this problem.