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)=
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)=
