Question

Determine a função derivada através da definição f(x) 3x² no ponto Xo = 2

Answer 1

Derivada no ponto

$\boxed{\boxed{\huge\displaystyle\mathsf{f'(x_{0})=\lim_{x \to x_{0}}\dfrac{f(x)-f(x_{0})}{x-x_{0}}}}}$

$\displaystyle\mathsf{f'(2)=\lim_{x \to 2}\dfrac{3{x}^{2}-12}{x-2}}\\\displaystyle\mathsf{f'(2)=\lim_{x \to 2}\dfrac{3({x}^{2}-4)}{x-2}}\\\displaystyle\mathsf{f'(2)=\lim_{x \to 2}\dfrac{3(x-2)(x+2)}{x-2}}\\\displaystyle\mathsf{f'(2)=\lim_{x \to 2}3(x+2)=3.(2+2)=3.4=12}$