How do you use the limit definition to find the derivative of $f (x) = 3 x - 4$ $f(x)=3x-4$ ?

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Answer 1 · 2017-05-18T14:49:21

$:. f'(x) = 3$

The definition of the derivative of $y=f(x)$ is

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

So Let $f(x) = 3x-4$ then;

$\ \ \ \ \ f(x+h) = 3(x+h) -4$
$:. f(x+h) = 3x+3h -4$

And so the derivative of $y=f(x)$ is given by:

$\ \ \ \ \ f'(x) = lim_(h rarr 0) ( (3x+3h -4) - (3x-4) ) / h$
$" " = lim_(h rarr 0) ( 3h ) / h$
$" " = lim_(h rarr 0) 3$
$:. f'(x) = 3$

How do you use the limit definition to find the derivative of f(x)=3x-4f(x)=3x−4f(x)=3x-4?