Barrons AP Calculus

1.

2.

3.

4.

5.

6.

7.

Part A

(A) Use the Rational    Function    Theorem;    the ratio   of  the coefficients    of

the highest power   of  x   is  .

(D) ,   so  .

(A) Since   f   ′(1)    =   0   and f   ′   changes from    negative    to  positive    there,  f

reaches a   minimum at  x   =   1.  Although    f   ′(2)    =   0   as  well,   f   ′   does    not

change  sign    there,  and thus    f   has neither a   maximum nor a   minimum at  x

=   2.

(C) ,   and .

(D).

(C) The graph   must    look    like    one of  these   two:

(D) F′(x)   =   3   cos x   cos 3x  −   sin x   sin 3x.