BUS 111 Lecture Notes - Lecture 1: Inflection Point, Inflection, Diminishing Returns
Document Summary
One question we can ask is how is the derivative changing? in other words, In fact, you could do this multiple times. Example: find f", f"", f""", and f(4) of x3+3x2-6. F4=0def: a curve is said to be concave down is the places where it is curving down (the tangent line i. e. the line with the derivative as its slope is above the curve). A curve is said to be concave up in the places where it"s curving up (where the tangent line is below the curve). An inflection point is the location where the curve changes concavity. Theorem: if f (x)>0, f is concave up at x. If f (x)<0, f is concave down at x. If f (x)=0, x is an inflection point (or worse). find f (x) 1. find the locations where f (x)=0, i. e. your inflection point candidates. 2: chose test points, plug in, and use the theorem.
