How would you find the Max and Min points on a graph?

Max and Mins occur where the slope of a graph equals zero. 

To find this, if we take the 1st derivative of a function and set the derivative equal to zero to solve for x. 

The values we solve for "x" are known as the critical points. Critical points are where the slope of the function is zero or undefined and the Max and Mins will occur at these points. 

Now we need to identify which of these points are the Max and Mins. To do this we plug in points in between our critical points. For Example if the critical points are -1 and 3. We would test the x values -1, 1 and 4 to see if the y values are negative or positive. It's important to note here these values are plugged into the origincal function (not the 1st derivative function we derived)

A Min will occur negative changing to postivie and a Max will be vise versa.  Using these plugged in x values we can see how the graph changes at these critical points to identify this.