How do you find f'(x) using the definition of a derivative $f (x) = x + 3$ $f(x) = x+3$ ?

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Answer 1 · 2015-11-03T17:15:50

Evaluate $f'(x) =lim_(hrarr0)(f(x+h)-f(x))/h$
to get $f'(x) = 1$

The definition of the derivative $f'(x)$ is
$color(white)("XXX")f'(x) = lim_(hrarr0)(color(red)(f(x+h))-color(blue)(f(x)))/h$

If $f(x) = x+3$
this becomes
$color(white)("XXX")f'(x)=lim_(hrarr0) (color(red)(((x+h)+3)) - color(blue)((x+3)))/h$

$color(white)("XXXXXX")=lim_(hrarr0) h/h$

$color(white)("XXXXXX")=lim_(hrarr0) 1$

$color(white)("XXXXXX")=1$

How do you find f'(x) using the definition of a derivative f(x) = x+3f(x)=x+3f(x) = x+3?