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#