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AP Calculus BC/Unit 7: Differential Equations
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Ordering Second Derivative Values
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Consider the particular solution $$y=\sqrt{4x^2+25}$$ to the differential equation $$\frac{dy}{dx}=\frac{4x}{y}$$. The second derivative is $$\frac{d^2y}{dx^2}=\frac{100}{(\sqrt{4x^2+25})^3}$$. The approximate values of the second derivative at $$x=0, 1, 2,$$ and $$3$$ are $$0.8, 0.642, 0.382,$$ and $$0.210$$, respectively. Which of the following lists the x-values in order from the smallest value of $$\frac{d^2y}{dx^2}$$ to the largest value?

A

2,3,1,0

B

0,1,2,3

C

3,1,2,0

D

3,2,1,0

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