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(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.
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