Ordering X-Values by Second Derivative
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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