
Stationary points
Hello all
I have a couple of questions.
First, if the first derivative of a function is a quadratic can I show that the function has no stationary points by showing that the discriminant of the first derivative is less than zero?
Second, how do I go about finding the range of the values of a for which
y = x  (a/x) has no stationary points.
I know the answer is that a is greater than or equal to zero, but I don't know how to get there.
Thank you.

Re: Stationary points
Yep, that's correct, no stationary points within the reals.
For the second question, what did you get as the derivative?

Re: Stationary points

Re: Stationary points
That is correct, what conditions can we put on 'a' for it to have zeros?
Think about a<0, a=0, a>0.

Re: Stationary points
Hello
I can see, I think, that if a = 0 then y=1 and that if a > 0, y > 1. When a < 0 I'm not sure.

Re: Stationary points
Quote:
Originally Posted by
Furyan When a < 0 I'm not sure.
In this case there will be zeros. pick a few values i.e a=1, 3, 100 etc. It will become clear.

Re: Stationary points
Yes it has, crystal. I don't know why I didn't just do that in the first place. Thank you for your help.