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How do you find the derivative of $f (x) = 3 x + 2$ $f(x)=3x+2$ using the limit process?

1 Answer

May 26, 2017

$f'(x)=3$

Explanation:

Recall that the derivative of any function $f(x)$ is given by:

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

Let $f(x)=3x-2$

$f'(x)=lim_(h->0)$ $((3(x+h)-2-(3x-2))/h)$

$=lim_(h->0)$ $((3x+3h-2-3x+2)/h)$

$=lim_(h->0)$ $((3h)/h)$

$=lim_(h->0)$ $(3)=3$

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