Thread: nature of turning points

dy/dx = (cos t - sin t)/(sin t - cos t)

The second derivative is 0.

I am trying to find the nature of turning points but the second derivative can't be used and a nature table can't be made because dy/dx always equals -1 for any value of t.

When , you have turning points. What can you deduce?

The turning points are where 0=cos t - sin t. I already have the points. How do I find their nature?

Originally Posted by Stuck Man

The turning points are where 0=cos t - sin t. I already have the points. How do I find their nature?

You clearly didn't read Quacky's Post.

Notice that

So the derivative is . You only have stationary points when the derivative is . What does this tell you about the function?

The curve is a spiral and it does have tuning points between 0<=t<=2pi. It is x=e^tsint, y=e^tcost.

The bottom line of dy/dx should have a plus symbol. I have finished this question now, thanks.

Originally Posted by Stuck Man

The bottom line of dy/dx should have a plus symbol. I have finished this question now, thanks.

This is why we always advise everyone to post the ENTIRE question, so that our correct guidance isn't completely useless.