Cracking The Ap Calculus ab Exam 2018

derivative  is  positive.   Therefore,  according   to  the second  derivative  test    (see    this    page),  the

perimeter   is  a   minimum at  r   =   .

5. 1,352.786 meters

Let’s   think   about   the situation.  If  the swimmer swims   the whole   distance    to  the cottage,    she will

be  traveling   the entire  time    at  her slowest speed.  If  she swims   straight    to  shore   first,  minimizing

her swimming    distance,   she will    be  maximizing  her running distance.   Therefore,  there   should

be  a   point,  somewhere   between the cottage and the point   on  the shore   directly    opposite    her,

where   the swimmer should  come    on  land    to  switch  from    swimming    to  running to  get to  the

cottage in  the shortest    time.

Let’s   draw    a   picture.

Let x   be  the distance    from    the point   on  the shore   directly    opposite    the swimmer to  the point

where   she comes   on  land.   We  have    two distances   to  consider.   The first   is  the diagonal    distance

that     the     swimmer     swims.  This    distance,   which   we’ll   call    D 1 ,   is  D 1 =  

. The second distance, which we’ll call D 2 , is simply D 2 =

1,800   −   x.  Remember    that    rate    ×   time    =   distance?   We’ll   use this    formula to  find    the total   time