Hello, shilz222!

If find points on curve where tangent is horizontal and vertical.

I got for horizontal tangents.

Is this correct? . . . . Yes!

First, we need

There is a formula for this, but we can derive it.

We know the conversion formulas: .

Then: .

. . Hence: .

Since and , we have: .

Divide top and bottom by

We have horizontal tangents when the numerator equals zero.

. .

. . Therefore: .

We have vertical tangents when the denominator equals zero.

. .

. . Therefore: .