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

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Answer 1 · 2016-05-21T14:26:20

$f'(x) =1-4x$ ,
see the derivation below.

By definition, the derivative of the function $f(x)$ is
$f'(x) = lim_(Delta x -> 0) (f(x+Delta x)-f(x))/(Delta x)$

In our case it looks like

$f'(x) =$
$= lim_(Delta x -> 0) (4+(x+Delta x)-2(x+Delta x)^2-4-x+2x^2)/(Delta x)=$

$= lim_(Delta x -> 0)(Delta x-4x Delta x-2(Delta x)^2)/(Delta x)=$

$= lim_(Delta x -> 0)(1-4x-2Delta x) =$

$= 1-4x - lim_(Delta x -> 0)(2Delta x) = 1-4x$

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