How do you find the turning points of a graph and how do you if the point is a maximum or a minimum?

Firstly you have to find the turning points of the graph. This is done by differentiating the equation of the line. Once you have found this first derivative, equate the equation to zero. Now solve the equation and find the x coordinates. Plug these x coordinates back into the original equation to find their corresponding y values. Now differentiate a second time. With this second derivative, plug in the x values of your turning points. If the result is negative, then the point is a maximum, if the result is positive, the point is a minimum and if it equals zero then the point is a point of inflection.