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How do you use the definition of a derivative function to calculate f'(4) where $f (x) = x + 3$ $f(x) = x+3$ ?

1 Answer

May 9, 2015

The derivative of $f (x)$ $f(x)$ :
$f'(x) = lim_(hrarr0) (f(x+h)-f(x))/h$

For $f(x) = x+3$
$f'(x) = lim_(hrarr0)((x+h+3)-(x+3))/h$

$= lim_(hrarr0) h/h$

$=lim_(hrarr0)1$

$=1$

Note that $f'(x) = 1$ for all values of $x$

So specifically
$f'(4) = 1$

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