Turning points are stationary points, there are two types of stationary points: turning and inflection. Turning being obviously change in gradient, while inflection being a change in concavity (I think lol).
To find the total number of stationary points dash the first equation and let that equal 0, hence finding the x values for the stationary points. This will be the x value for the coordinate of the max point. Sub into original equation to acquire the y coordinate.
Now to test for max or min, there are two ways: One is a sure fire method, but a tad more tedious, while the other is easier but sometimes does not work in some cases (when the double dashed equals 0 I think).
The easier method:
Dash the first equation twice in order to obtain a numerical value in which >0 is equal to a min point and <0 is a max point.
The second better method:
Since you know the x value of the turning points (in which its gradient equals to zero), test if there is a change in gradient. So basically x-e (to discover if the gradient left of the stationary point is positive or negative) and sub that into the dashed equation to discover the gradient and then x+e (to determine the gradient, at right of the stationary point). Where e= any small numerical value you can choose (generally 0.001 or something, just as long as it's small enough to not pass another stationary point).
Btw put this in a table form as it is a lot easier to see. Then for every y' value discovered by subbing in the x-e/x+e put it in the table and determine where it is positive or negative. Giving a positive gradient a "/" so you know it is rising. And a negative gradient "\" so you know it is decreasing.
Eventually you see a pattern
\ -- / = min turning point
/ -- \ = max turning point
--=the gradient of the stationary point, which is 0.
&space;=7-4x-x^2)
has one turning point. Find its coordinates and show that it is a maximum turning point. 
