Below is the graph of a function y fx with several points l

Below is the graph of a function y = f(x) with several points labeled. Complete the chart by determining at each point whether each of y, y\' and y\" is positive (+), negative (-), zero (0), or undefined (UNDEF). Which (if Any) of the points are local maxima? Which (if any) of the points are local minima? Which (if any) of the points are inflection points?

Solution

a)

y is positive or negative if y is above or below x axis respectively

y\' is positive or negative if y is increasing or decreasing with increasing x respectively

y\'\' is positive if y is concave up,y\'\' is negative if y is concave down,y\'\'=0 at point of inflection

Point                     y                               y\'                                y\'\'

A                                 -                                        +                                        +

B                                 +                                       UNDEF                              UNDEF

C                                 -                                        0                                        +

D                                 +                                        +                                       0

E                                 +                                        0                                        -

F                                 +                                        -                                        -

b)

B,E

c)

A and C

d)

D