How can I remember when a turning point of a function is a maximum or a minimum?

The key is to look at the first and second derivatives of that function. Remember that a turning point always has the first derivative equal to zero. Then, the sign of the second derivative indicates if that turning point is either a maximum or a minimum. If the second derivative is negative than remember that the shape of the function resembles a hill (the function is concave) and the highest point can only be a maximum as the function decreases on both sides. If the second derivative is positive, then the graph of the function looks like a cavity (the function is convex) and the turning point is a minimum as its the lowest lying point of that function.