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

Then, also using the Racetrack Principle, what quadratic function

*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.