x Turn on thread page Beta
 You are Here: Home >< Maths

Stationary Point Inequality Question watch

I don't get how we step from the stationary point expression equalling zero, to the inequality. Maybe it is the discriminant, but it is two stationary points!!
2. (Original post by Gmart)

I don't get how we step from the stationary point expression equalling zero, to the inequality. Maybe it is the discriminant, but it is two stationary points!!
Not quite sure what you are saying but this is indeed a use of the discriminant.

We require 2 real roots of the equation and for this to occur .
3. (Original post by Gmart)

I don't get how we step from the stationary point expression equalling zero, to the inequality. Maybe it is the discriminant, but it is two stationary points!!
At the stationary points dy/dx = 0. From this we get the quadratic which equals zero. For there to be two stationary points, this equation must have two solutions, this is where the discriminant comes in.
4. But the discriminant just has one inequality sign, the answer has two!!!

And the discriminant is about having two roots, not two stationary points, and a quadratic only has one stationary point anyway.
5. (Original post by Gmart)
But the discriminant just has one inequality sign, the answer has two!!!

And the discriminant is about having two roots, not two stationary points, and a quadratic only has one stationary point anyway.
You don't understand.

Once you differentiated the numerator of the expression must be equal to zero.

ie.

This determines the x-coordinates of the points at which you have stationary points. You want 2 stationary points, therefore you want this equation to give you two values of x. The equation must have two distinct roots. We use the discriminant.

Sketch the curve on the LHS, and determine the points at which it intersects the x-axis. Now look for the region where the curve is below the x-axis. Does that help?
6. (Original post by Ateo)
You don't understand.

Once you differentiated the numerator of the expression must be equal to zero.

ie.

This determines the x-coordinates of the points at which you have stationary points. You want 2 stationary points, therefore you want this equation to give you two values of x. The equation must have two distinct roots. We use the discriminant.

Sketch the curve on the LHS, and determine the points at which it intersects the x-axis. Now look for the region where the curve is below the x-axis. Does that help?
That sure does!!

Thank you so much, I have been working myself up into a tizz about that for an embarrassing amount of time :O

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: April 4, 2013
Today on TSR

How much will your degree earn you?

Find out where yours ranks...

Poll
Useful resources

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

How to use LaTex

Writing equations the easy way

Study habits of A* students

Top tips from students who have already aced their exams

Chat with other maths applicants