The derivative of a function gives us the slope of the curve of that function at any given point. Look for the peaks and valleys (as mentioned)...those have a slope of zero and therefore the graph of its derivative should cross the x-axis at that point.
Also look for where the curve of the function is steepest, the corresponding derivative curve will be a high positive or negative value depending on whether the function is increasing or decreasing.
Lastly, look for functions that are not continuous (not a smooth curve). A break in a smooth curve will not have a derivate at that point, therefore, not-continuous.