Step 1: First Derivative Test Derivative Interpretation: The first derivative f ( x ) f (x) of a function f ( x ) f(x) gives us information about the slope of the function at any point x x: If f ( x ) = 0 f (x)=0, there is a critical point, which could indicate a local maximum, local minimum, or a saddle point. This is because the slope is flat at that point. If f ( x ) > 0 f (x)>0, the function is increasing. If f ( x ) 0 f (x)>0, the graph of the function is concave up (like a cup), which indicates that the critical point is a local minimum. Concave Down: If f ( x )