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AP Calculus BC/Unit 7: Differential Equations
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Ordering X-Values by Second Derivative
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For the solution to $$\frac{dy}{dx}=\frac{4*x}{y}$$ with solution $$y=\sqrt{4*x^2+25}$$, the second derivative is given by $$\frac{d^2y}{dx^2}=\frac{100}{(\sqrt{4*x^2+25})^3}$$. Evaluating this expression gives approximately:
At x = -3: 0.210,
At x = -1: 0.642,
At x = 1: 0.642,
At x = 3: 0.210.
Rank the x-values in increasing order of the second derivative. When values are equal, list the smaller x first. Express your answer as an ordering of the x-values separated by commas.

A

-1,1,-3,3

B

1,-1,3,-3

C

-3,3,-1,1

D

3,-3,-1,1

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