BUS 111 Lecture Notes - Lecture 12: If And Only If
Document Summary
Def: let f be a function defined on some interval, [a,b], and let c be an x value in that interval. F(c) is an absolute maximum if f(c)(cid:951)f(x) for any other x value. F(c) is an absolute minimum if f(c)(cid:950)f(x) for any other x value. If f is a continuous function on a closed interval, [a,b], then f has both an absolute max and absolute min occurring somewhere on [a,b]. In fact, they will occur at a critical value or an endpoint of the interval. Finding maxes and mins method: take a derivative, find the critical values, plug the critical values into the original function, plug the endpoints into the original function, decide which is a max and which is a min. Note: to find absolute extreme, we plug into the original function. To find local extrema, we plug into the derivative. Example: find the absolute extrema of f(x)=x3-3x+1 on the interval [-3,1. 5]
