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AP Calculus AB/Unit 7: Differential Equations
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Ordering Second Derivative Values

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For the differential equation $$\frac{dy}{dx}=\frac{4*x}{y}$$ with solution $$y=\sqrt{4*x^2+25}$$, the second derivative is computed as
$$\frac{d^2y}{dx^2}=\frac{100}{(\sqrt{4*x^2+25})^3}.$$
The approximate values are: at x = 0: ~0.8; x = 1: ~0.642; x = 2: ~0.382; x = 3: ~0.210.
Rank the x-values in order of increasing second derivative (i.e. from least concave upward to most concave upward). Write your answer as an ordering of x-values separated by commas.

A

0,1,2,3

B

3,2,1,0

C

2,3,1,0

D

3,1,2,0

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