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

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Consider the particular solution y=4x2+25y=\sqrt{4x^2+25} to the differential equation dydx=4xy\frac{dy}{dx}=\frac{4x}{y}. The second derivative is d2ydx2=100(4x2+25)3\frac{d^2y}{dx^2}=\frac{100}{(\sqrt{4x^2+25})^3}. The approximate values of the second derivative at x=0,1,2,x=0, 1, 2, and 33 are 0.8,0.642,0.382,0.8, 0.642, 0.382, and 0.2100.210, respectively. Which of the following lists the x-values in order from the smallest value of d2ydx2\frac{d^2y}{dx^2} to the largest value?

A

0,1,2,3

B

3,2,1,0

C

2,3,1,0

D

3,1,2,0

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