Information Economics with Real Estate Applications

Appendix A Additional material

A.1 Derivatives

Let f (x) be a function taking a number x and transforming it into the number f (x). As a concrete example take the function f (x) = 1 + 4x − x². This function is plotted in Figure A.1.

Figure A.1: Derivatives I.

We now ask the following question: What is the slope of the function at a point (x, f (x))? The slope of a function at the point (x, f (x)) is defined to be the slope of the straight line that is tangental to the function at the point (x, f (x)). For the function f (x) = 1 +4x − x², the tangental lines of the function at the points (0, 1) and (3, 4) are plotted in the graph in Figure A.1 ...