Well finding the slope of an equation at a given point is definately something that people do everyday.
A friend of mine tests irrigation units for flow.
He has data collected for for units and plots them on a flow versus pressure graph. He then has excell give him an equation to fit the data.
Their are certain kinds of irrigation units which give the same flow over a range of pressure and over that range the slope of the line should be zero. He checks the slope at any given point within that range using precalculus techniques.
So engineers, statisticians, and anyone else plotting data and fitting an equation to that data could be using precalculus techniques to analyze that data.