- #1

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- Homework Statement
- A curve is defined parametrically by

$$x=-(t^2+4)^{\frac{1}{2}} , y=\frac{\ln t}{t}$$

Find the turning point and explain why it is maximum

- Relevant Equations
- Derivative

Second derivative to check the nature

Sign Diagram

I have found the turning point. I want to ask how to check the nature of the turning point.

My idea is to change the equation into cartesian form then find the second derivative and put the ##x## value of the turning point. If second derivative is positive, then it is minimum and if the second derivative is negative, then it is maximum.

I want to ask whether there is other method to check the nature, maybe directly using the parametric equation (without changing it into cartesian equation).

Thanks

My idea is to change the equation into cartesian form then find the second derivative and put the ##x## value of the turning point. If second derivative is positive, then it is minimum and if the second derivative is negative, then it is maximum.

I want to ask whether there is other method to check the nature, maybe directly using the parametric equation (without changing it into cartesian equation).

Thanks