How do you use the limit definition of the derivative to find the derivative of $y=-4x-2$ ?

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Answer 1 · 2016-09-12T07:53:32

$-4$

The definition of derivative is stated as follows:
$lim(h->0)(f(x+h)-f(x))/h$

Let's apply the above formula on the given function:

$lim(h->0)(f(x+h)-f(x))/h$
$=lim(h->0)(-4(x+h)-2-(-4x-2))/h$
$=lim(h->0)(-4x-4h-2+4x+2)/h$
$=lim(h->0)((-4h)/h)$

Simplifying by $h$

= $lim(h->0)(-4)$
$=-4$

How do you use the limit definition of the derivative to find the derivative of y=-4x-2y=-4x-2?