Beginner. Working on this problem: Use the definition of a derivative function to calculate f'(4) where f(x) = x + 3.
Have made attempt using lim h->0 [f(x+h) - f(x)]/h but unsure if answer is correct. Need explanation. Help!
There is an equivalent definition that is sometimes useful:
$\displaystyle f'(c) = \lim_{x \to c} \frac {f(x) - f(c)}{x-c} $
so $\displaystyle f'(4) = \lim_{x \to 4} \frac {f(x) - f(4)}{x-4} $ $\displaystyle = \lim_{x \to 4} \frac {(x+3) -7}{x-4} $ $\displaystyle = \lim_{x \to 4}\frac {x-4}{x-4} = 1 $