Using the limit definition, how do you differentiate $f (x) = 4 - 2 x - x^{2}$ $f(x)=4 -2x -x^2$ ?

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Answer 1 · 2016-12-27T13:27:28

$f'(x) = -2-2x$

The limit definition of the derivative states that:

$f'(x) = lim_(Deltax->0) (f(x+Deltax)-f(x))/(Deltax)$

For $f(x)= 2-2x-x^2$ we have:

$f'(x) = lim_(Deltax->0) ((2-2(x+Deltax)-(x+Deltax)^2)-(2-2x-x^2))/(Deltax)$

$f'(x) = lim_(Deltax->0) ((2-2x-2Deltax-x^2-2xDeltax-(Deltax)^2-2+2x+x^2))/(Deltax)$

$f'(x) = lim_(Deltax->0) ((-2Deltax-2xDeltax+(Deltax)^2))/(Deltax)$

$f'(x) = lim_(Deltax->0) (-2-2x+Deltax)=-2-2x$

Using the limit definition, how do you differentiate f(x)=4 -2x -x^2f(x)=4−2x−x2f(x)=4 -2x -x^2?