document.write( "Question 1199793: Determine the zeros of f(x)=x^2-3x-4 and estimate the instantaneous rate of change in f(x) at the zeros \n" ); document.write( "

Algebra.Com's Answer #833762 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "(a)  Determine the zeroes of f(x) = x^2 -3x - 4 by factoring\r\n" );
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document.write( "         f(x) = x^2 -3x - 4 = (x-4)*(x+1),\r\n" );
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document.write( "     so the zeroes are x= -1  and  x= 4.\r\n" );
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document.write( "(b)  To estimate the instantaneous rate of change in f(x) at the zeros,\r\n" );
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document.write( "     first calculate the derivative f'(x) of f(x):  f'(x) = 2x-3.\r\n" );
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document.write( "     Then calculate the values of f'(x) at x= -1 and x= 4:\r\n" );
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document.write( "          f'(-1) = 2*(-1)-3 = -2 - 3 = -5;\r\n" );
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document.write( "          f'(4)  = 2*4 - 3 = 8 - 3 = 5.\r\n" );
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document.write( "     ANSWER.  The instantaneous rate of change in f(x)  at  x= -1 is  -5;\r\n" );
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document.write( "              The instantaneous rate of change in f(x)  at  x= 4  is   5.\r\n" );
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