Uriah Oconnor

Mathematics

18 July, 07:53

Racetrack Principle

Suppose that f (t) is continuous and twice-differentiable for t≥0. Further suppose f″ (t) ≥7 for all t≥0 and f (0) = f′ (0) = 0.

Using the Racetrack Principle, what linear function g (t) can we prove is less than or equal to f′ (t) (for t≥0) ?

g (t) =

Then, also using the Racetrack Principle, what quadratic function h (t) can we prove is less than or equal to than f (t) (for t≥0) ?

h (t) =