# 4.3 how dx affect shape of graph

 inflection point any value of x where concavity changesmore formally, point P on y = f(x) if f(x) is continuous @ that point if curve changes from CU to CD or from CD to CU @ P increasing/decreasing test f'(x) is +: f(x) is increasingf'(x) is - : f(x) is decreasing first dx test local max @ c: if f'(x) changes from + to - @ clocal min @ c: if f'(x) changes from - to + @ cnone @ c:  if f'(x) does not change sign @ c concave upward if graph of f(x) lies above all its tangents on an interval I concave downward if graph of f(x) lies below all its tangents on an interval I second dx test helps determine * intervals of concavity* max & min values concavity test concave up on I:  f"(x) + for all x in Iconcave down on I: f"(x) - for all x in I second dx test f"(x) is continuous near clocal max @ c: if f'(c) = 0 & f"(c) +local min @ c: if f'(c) = 0 & f"(c) - inconclusive second dx test when f"(c) = 0 or when f"(c) dnemax, min, or neither T/F: if f'(x) is increasing, f(x) is + if f'(x) is decreasing, f(x) is - F: inverse/backwards correct: if f(x) is increasing, f'(x) is +if f(x) is decreasing, f'(x) is - T/F: if f(x) is increasing, f'(x) is + if f(x) is decreasing, f'(x) is - T What does f'(x) say about f(x)? What does f"(x) say about f(x)? Authorjojobean0203 ID215009 Card Set4.3 how dx affect shape of graph Descriptionhow dx affect shape of graph Updated2013-04-22T07:11:18Z Show Answers