Math 111 Test 3 Terms

Critical number : x=c is a critical number for a function f(x) if: 1) x=c is in the domain of f (graphically, it is a point on the graph)2) f'(c)=0 OR f'(c) DNE (discontinuous, sharp corner/cusp, or vertical tangent line)Graphically, it will have a horizontal tangent line at the critical number(s)

Absolute maximum : Let c be a number in the domain, D, of a function f. Then f(c) is:an absolute maximum if f(c) is greater than or equal to f(x) for all x in D

Inflection point : The point (x,y) is an inflection point for a function f(x) if f changes concavity at (x,y) as in continuous near the point.

Concavity test : If f"(x)<0 on an interval, then f is CD on the interval.If f"(x)>0 on an interval, then f is CU on the interval.