find maximum and minimum value of f(x)=x2-3x-4/x-8

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Please find below the solution to the asked query:

We have:fx=y=x2-3x-4x-8dydx=x-8ddxx2-3x-4-x2-3x-4.ddxx-8x-82=x-82x-3-x2-3x-4x-82=2x2-3x-16x+24-x2+3x+4x-82=x2-16x+28x-82=x2-14x-2x+28x-82=x-2x-14x-82For maxima or minima, dydx=0, hencex-2x-14x-82=0x=2 and x=14.One value will give local minima while other will give local maxima.fx=x2-3x-4x-8f2=4-6-42-8=1f14=196-42-414-8=1506=25Nowf'x>0 when x-,214, and f'x<0 when x2,14Hence fx increases when  x-,2, then decreases when x2,14 and again increases when x14,.Hence x=2 is point of local maxima and x=14 is a point of local minima.Note: Here global maximum and minimum value cannot be determined.

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