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" ... In some ways, the fundamental thing to know about differential calculus is that the tangent line to the graph of a function is a decent approximation to the function itself, provided you don't move too far away from the point of tangency. How do you find the equation of this line? It's simple if you know a point (which you do, the point of tangency) and the slope of the line. The latter is by definition the derivative of the function at the point. So while I could bust out my calculator and compute √144.5, I prefer to just do the linear approximation, which I can do in my head for this function now that I've been teaching calculus for 20+ years. ... "