Question

Determine a função derivada através da definição; f(x) = x² - 8x + 9

Por favor preciso de ajuda!

Answer 1

$\underset{h\to0}{\lim}\ \dfrac{f(x+h)-f(x)}{h}=\\\\\\\underset{h\to0}{\lim}\ \dfrac{(x+h)^2-8(x+h)+9-(x^2-8x+9)}{h}=\\\\\\\underset{h\to0}{\lim}\ \dfrac{x^2+2xh+h^2-8x-8h+9-x^2+8x-9}{h}=\\\\\\\underset{h\to0}{\lim}\ \dfrac{2xh+h^2-8h}{h}=\underset{h\to0}{\lim}\ 2x+h-8=\boxed{2x-8}$