Suppose that f (t) f (t) is continuous and twice-differentiable for t≥0t≥0. further suppose f′′ (t) ≤3f″ (t) ≤3 for all t≥0t≥0 and f (0) = f′ (0) = 0f (0) = f′ (0) = 0. using the racetrack principle, what linear function g (t) g (t) can we prove is greater than or equal to f′ (t) f′ (t) (for t≥0t≥0) ?

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Ortiz

Mathematics

4 July, 19:49

Suppose that f (t) f (t) is continuous and twice-differentiable for t≥0t≥0. further suppose f′′ (t) ≤3f″ (t) ≤3 for all t≥0t≥0 and f (0) = f′ (0) = 0f (0) = f′ (0) = 0. using the racetrack principle, what linear function g (t) g (t) can we prove is greater than or equal to f′ (t) f′ (t) (for t≥0t≥0) ?

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Alisha Moon · Answer 1

(x) is continuous and twice differentiable for ±≥ 0. Suppose f" (±) ≤ 5 for all ±≥ 0 and f (0) = f’ (0) = 0. The linear function with a derivation of 0 is y = 0. Thus we have g (t) = 0. The quadratic function with concavity 5 and initial slope 0 is y = 5/2 x^2 + 0x. Therefore, h (t) = (5/2) x^2