Ordering Second Derivative Values
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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