Question

Ao calcularmos a derivada da função f(x) = 5x² (pela definição) para x = 1, encontramos como resultado:

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10

9

12

8

11

Answer 1

$\Large\boxed{\begin{array}{l}\underline{\rm De~\!\!finic_{\!\!,}\tilde ao\,de\,derivada\,no\,ponto}\\\displaystyle\sf f'(p)=\lim_{x \to p}\dfrac{f(x)-f(p )}{x-p}\end{array}}$

$\Large\boxed{\begin{array}{l}\sf f(x)=5x^2\\\sf f(1)=5\cdot1^2=5\cdot1=5\\\displaystyle\sf f'(1)=\lim_{x \to 1}\dfrac{5x^2-5}{x-1}\\\\\displaystyle\sf f'(1)=\lim_{x \to 1}\dfrac{5\cdot(x^2-1)}{x-1}\\\\\displaystyle\sf f'(1)=\lim_{x \to 1}\dfrac{ 5\cdot\diagup\!\!\!\!\!(x-\diagup\!\!\!\!\!1)(x+1)}{\diagup\!\!\!\!\!(x-\diagup\!\!\!\!\!1)}\\\\\displaystyle\sf f'(1)=5\lim_{x \to 1}(x+1)\end{array}}$

$\Large\boxed{\begin{array}{l}\sf f'(1)=5\cdot (1+1)\\\sf f'(1)=5\cdot 2\\\sf f'(1)=10\end{array}}$