Barrons AP Calculus

AB/BC 1.

Part A

This    is  the graph   of  f   ′(x).

(a) f   is  increasing  when    f   ′(x)    >   0.  The graph   shows   this    to  be  true    in  the

interval    a   <   x   <   b.  Use the calculator  to  find    a   and b   (where  ex  −   2

cos 3x  =   0); then    a   =   0.283   <   x   <   3.760   =   b.

(b) See signs   analysis.

Since   f   decreases   to  the right   of  endpoint    x   =   0,  f   has a   local

maximum at  x   =   0.  There   is  another local   maximum at  x   =   3.760,

because f   changes from    increasing  to  decreasing  there.

(c) See signs   analysis.