BUS 111 Lecture Notes - Lecture 1: Maxima And Minima
Document Summary
Definition: let c be a number in the domain of f, then f(c) is a relative maximum if there is some open interval around c such that f(c) f(x) for any other x in the interval. Similarly, we say that f(c) is a relative minimum if there is some open interval around c such that f(c) f(x) for any other x in the interval. Note: we also use the phrases local maximum (max) and local minimum (min) . Together, we refer to relative maxima and minima as relative extrema. Theorem: if f has a relative extrema, f(c), then c is a critical value [ or an endpoint of the domain]. Method: first derivative test: find the derivative, find the critical values (set =0 and solve for x, chose test points on either side of the critical values and determine increasing or decreasing. If f" changes from positive to negative at the critical value, you have a.
