Finding Stationary Points

Stationary Points

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Find the stationary points of

First differentiate, using the general rule		and say that the result must equal 0
This gives a quadratic, which can be factorized.
So, the stationary points are at
We need to know the y co-ordinates. We find these by substituting the values of x back into y.

Now we need to know what type of stationary point we have. This sometimes referred to as Determining the nature.
To do this we look at the gradient around the stationary point.
Choose 2 easy values of x, one each side of the point, but not past the other point, and determine the gradient.
To the left of the point the gradient is negative
To the right the gradient is positive
A quick sketch shows that the point is a minimum

Now look at the second stationary point
and determine it's nature. We already know that the gradient to the right is negative,( from x = 0)
So this point is a maximum

Therefore the two stationary points on the curve
are a minimum at
and a maximum at

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