BUS 111 Lecture Notes - Lecture 13: Product Rule, Inflection, Inflection Point
Document Summary
One question we can ask is (cid:498)how is the derivative changing? (cid:499) )n other words, find the derivative"s derivative. )n fact, you could do this multiple times. Example: find f", f"", f""", and f(4) of x3+3x2-6. F"""=(cid:888) is said to be concave up in the places where it"s curving up (cid:523)where the tangent line is. Def: 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). An inflection point is the location where the curve changes concavity. Concave up at (0, : chose test points, plug in, and use the theorem. Example: find the inflection points and critical values for f(x)=-x3-12x2-45x+2. Answer: local min at x=-5, inflection point at x=-4, and local max at x=-3. Theorem: if f(cid:499)(cid:523)x(cid:524)>(cid:882), f is concave up at x. )f f(cid:499)(cid:523)x(cid:524)<0, f is concave down at x.
