4.3 how dx affect shape of graph
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inflection point
 any value of x where concavity changes
 more 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 increasing
 f'(x) is  : f(x) is decreasing

first dx test
 local max @ c: if f'(x) changes from + to  @ c
 local min @ c: if f'(x) changes from  to + @ c
 none @ 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 I
 concave down on I: f"(x)  for all x in I

second dx test
 f"(x) is continuous near c
 local 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) dne
 max, 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)?