(a)  Determine the zeroes of f(x) = x^2 -3x - 4 by factoring

         f(x) = x^2 -3x - 4 = (x-4)*(x+1),

     so the zeroes are x= -1  and  x= 4.



(b)  To estimate the instantaneous rate of change in f(x) at the zeros,

     first calculate the derivative f'(x) of f(x):  f'(x) = 2x-3.


     Then calculate the values of f'(x) at x= -1 and x= 4:

          f'(-1) = 2*(-1)-3 = -2 - 3 = -5;

          f'(4)  = 2*4 - 3 = 8 - 3 = 5.


     ANSWER.  The instantaneous rate of change in f(x)  at  x= -1 is  -5;

              The instantaneous rate of change in f(x)  at  x= 4  is   5.