Concavity of Parametric Equations

[sheldonrocks97]

Homework Statement

Find dy/dx and d^y/dx^2

x=e^t; y=te^(-t)

For which values of t are concave upward? (write your answer in interval notation).

Homework Equations

The Attempt at a Solution

I used the formula to find d^2y/dx^2.

d^2y/dx^2= e^(-3t)*(2t-3)

Set it to zero:

e^(3t)*(2t-3)>0

I solved it and got t>3/2, but the computer told me it was wrong. What am I doing wrong here?

 

[LCKurtz]

Homework Statement

Find dy/dx and d^y/dx^2

x = cos 2t, y = cos t, 0 < t < ∏

For which values of t are concave upward? (write your answer in interval notation).

Homework Equations

The Attempt at a Solution

I used the formula to find d^2y/dx^2.

d^2y/dx^2= e^(-3t)*(2t-3)

I solved it and got t>3/2, but the computer told me it was wrong. What am I doing wrong here?

Where did the exponential come from? You only have cosines in the problem. After you fix that, please show your work so we can follow it.

 

[Mark44]

Where did the exponential come from?

The OP edited his post, so the parametric equations now have exponential form

After you fix that, please show your work so we can follow it.

Yes. Show your work for dx/dt and dy/dt and so on.