Second Derivative of Parametric Equations

Question

The table below defines four curves with parametric equations. Which of the following correctly orders the curves from least to greatest according to the value of their second derivative, $$\frac{d^2y}{dx^2}$$, evaluated at $t=1$?

| Curve   | Parametric Equations            |
|---------|---------------------------------|
| Curve 1 | $$x=t, \quad y=t^2$$             |
| Curve 2 | $$x=t, \quad y=t^3$$             |
| Curve 3 | $$x=t, \quad y=\sqrt{t}$$        |
| Curve 4 | $$x=t, \quad y=\ln(t)$$          |

Accepted Answer

Curve 4, Curve 3, Curve 1, Curve 2

Answer

Curve 1, Curve 3, Curve 4, Curve 2

Answer

Curve 4, Curve 1, Curve 3, Curve 2

Answer

Curve 3, Curve 4, Curve 1, Curve 2

Curve	Parametric Equations
Curve 1	$x=t, \quad y=t^2$
Curve 2	$x=t, \quad y=t^3$
Curve 3	$x=t, \quad y=\sqrt{t}$
Curve 4	$x=t, \quad y=\ln(t)$

Second Derivative of Parametric Equations

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