Question

Qual é a equação da reta tangente ao gráfico de f(x) = 2x no ponto de abscissa -1?
• A)
y = 6x +9
• B)
y=x-9
• C)
y = -6x - 8
• D)
y = 6x + 4
• E)
y = 2x + 6

Answer 1

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

$\boxed{\begin{array}{l}\sf y=-2+2\cdot(x-(-1))\\\sf y=-2+2\cdot (x+1)\\\sf y=-2+2x+2\\\red{\sf y=2x}\\\sf revise~o~gabarito.\end{array}}$