How do you use the limit definition of the derivative to find the derivative of $f(x)=3x-7$ ?

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Answer 1 · 2016-12-15T21:34:34

$f'(x) = 3$

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

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

So Let $f(x) = 3x-7$ then;

$\ \ \ \ \ f(x+h) = 3(x+h) -7$
$:. f(x+h) = 3x+3h -7$

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

$\ \ \ \ \ f'(x) = lim_(h rarr 0) ( (3x+3h -7) - (3x-7) ) / h$
$" " = lim_(h rarr 0) ( 3h ) / h$
$" " = lim_(h rarr 0) 3$
$:. f'(x) = 3$

How do you use the limit definition of the derivative to find the derivative of f(x)=3x-7f(x)=3x-7?