Question

Encontre a derivada da função f(x) = x2 −4x pr denição

Answer 1

Explicação passo-a-passo:

$\displaystyle\lim_{\Delta \to 0}\sf{\dfrac{f(x+\Delta )-f(x)}{\Delta}}$

f(x) = x²- 4x

$\iff\displaystyle\lim_{\Delta \to a}\sf{\dfrac{ (x+\Delta)^2-4(x+\Delta) - (x^2-4x) }{\Delta}}$

$\iff\displaystyle\lim_{\Delta\to 0}\sf{\dfrac{\cancel{x^2}+2x\Delta + \Delta^2\cancel{-4x}-4\Delta \cancel{- x^2}+\cancel{4x}}{\Delta}}$

$\iff\displaystyle\lim_{\Delta\to 0}\sf{\dfrac{2x\Delta + \Delta^2-4\Delta}{\Delta}}$

$\iff\displaystyle\lim_{\Delta \to 0}\sf{\dfrac{\cancel{\Delta}(2x+\Delta - 4)}{\cancel{\Delta}}}$

$\iff\displaystyle\lim_{\Delta \to 0}\sf{(2x+\Delta - 4)}$

$~~~~~\sf{=2x+0-4 }$

$~~~~~\sf{~=~2x - 4 }$

This answer was elaborad by:

MURRIMA , JOAQUIM MARCELO

UEM(MOÇAMBIQUE)-DMI