Question

Consider the curve x(t) = t^3 − 4t and y(t) = t^2. Determine where the curve has a horizontal tangent.

Answer 1

I got (0,0)

Answer 2

You get a horizontal tangent when dy/dt=0 AND dx/dt <> 0 (not zero).

dy/dt=2t=0 if t=0.
dx/dt=3t²-4. If t=0, then dx/dt=-4, so that is ok.

If t=0 there is a horizontal tangent. x(0)=0, y(0)=0, so it is (0, 0).

Well done!

Answer 3

Awesome! Thank you so much!

Answer 4

YW!

You said you got (0, 0). Did you find that in the same way I did?

Answer 5

I found dy/dx. I did this by getting dy/dt=2t and dx/dt=3t^2-4

Answer 6

Then I did (dy/dt)/(dx/dt)=dy/dx=2t/(3t^2-4)

Answer 7

then I solved 2t=0

Answer 8

made sure t=0 was in my domain

Answer 9

then plugged it into x(t) and y(t) to get my point

Answer 10

So, yes. I think it's the same.

Answer 11

:D