parametric equations of a curve

A curve: x=(1+t)^0.5, y=(1-t)^-0.5

After plotting the curve I don't see any turning points. I can see a vertical asymptote at x=2^0.5.

I have calculated that there is a stationary point at t=-1 and the point (0,2^-0.5). I don't see it on the graph though. At that point the second derivative is 0.25*(2^0.5) and hence greater than 0 and there is a minimum turning point.

The answers give the point (0,2^0.5) and says it is a minimum end point.

Re: parametric equations of a curve

Quote:

Originally Posted by

**Stuck Man** I don't see it on the graph though.

The point, or it looking like a starionary point? It's there.

Quote:

Originally Posted by

**Stuck Man** The answers give the point (0,2^0.5)

Must be a typo.

Quote:

Originally Posted by

**Stuck Man** and says it is a minimum end point.

i.e. would be a minimum turning point if it wasn't an end point.

Re: parametric equations of a curve

Left of the supposed stationary point the graph slope down slightly as if there is a horizontal asymptote. The point is not an end point.

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Re: parametric equations of a curve

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Re: parametric equations of a curve

Quote:

Originally Posted by

**Stuck Man** A curve: x=(1+t)^0.5, y=(1-t)^-0.5

After plotting the curve I don't see any turning points. I can see a vertical asymptote at x=2^0.5.

I have calculated that there is a stationary point at t=-1 and the point (0,2^-0.5). I don't see it on the graph though. At that point the second derivative is 0.25*(2^0.5) and hence greater than 0 and there is a minimum turning point.

The answers give the point (0,2^0.5) and says it is a minimum end point.

1. You certainely have determined that

2. Your curve is the right branch (drawn in red) of the graph of (drawn in green)

3. Obviously the left end point is a minimum with a horizontal tangent.

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Re: parametric equations of a curve

You can see that is a minimum.

Re: parametric equations of a curve

My graphing program is displaying an incorrect line on the left of x=0. It is GraphCalc from 2003. Is there any others you know about?

Re: parametric equations of a curve