Ranking Second Derivative Values from a Table

Question

Let $$y$$ be the solution to the differential equation $$\frac{dy}{dx}=(x+1)*y$$, with the second derivative given by $$\frac{d^2y}{dx^2}=y*((x+1)^2+1)$$. The following table provides approximate values for the solution and its second derivative at several values of $$x$$.

| x | y = e^(x²/2 + x) (approx.) | Second Derivative Calculation |
|---|---------------------------|-----------------------------|
| 0 | 1                         | (1)*((1)²+1) = 2            |
| 1 | ~4.48                     | ~4.48*((2)²+1) ≈ 22.41        |
| 2 | ~54.60                    | ~54.60*((3)²+1) ≈ 546         |
| 3 | ~1808                     | ~1808*((4)²+1) ≈ 30736        |

Using the information from the table, which of the following lists the $$x$$-values in decreasing order of the corresponding values of the second derivative?

Accepted Answer

3,2,1,0

Answer

0,1,2,3

Answer

3,1,2,0

Answer

2,3,1,0

x	y = e^(x²/2 + x) (approx.)	Second Derivative Calculation
0	1	(1)*((1)²+1) = 2
1	~4.48	~4.48*((2)²+1) ≈ 22.41
2	~54.60	~54.60*((3)²+1) ≈ 546
3	~1808	~1808*((4)²+1) ≈ 30736

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