Using-the-definition-calculate-the-derivative-at-point-x-2-f-x-2x-3-

Question Number 69979 by Maclaurin Stickker last updated on 29/Sep/19

U s i n g t h e d e f i n i t i o n c a l c u l a t e t h e

d e r i v a t i v e a t p o i n t x = 2

f (x) = 2 x^{3}

Commented by kaivan.ahmadi last updated on 29/Sep/19

{l i m}_{x \to 2} \frac{f (x) - f (2)}{x - 2} = {l i m}_{x \to 2} \frac{2 x^{3} - 16}{x - 2} =

{l i m}_{x \to 2} \frac{2 (x - 2) (x^{2} + 2 x + 4)}{x - 2} = {l i m}_{x \to 2} 2 (x^{2} + 2 x + 4) =

2 (4 + 4 + 4) = 24

Commented by Rio Michael last updated on 29/Sep/19

f^{^{'}} (x) = 6 x^{2} \Rightarrow f^{^{'}} (2) = 24