Question

Find the derivative of f(x) = 6x + 2 at x = 1. 1 2 3 6

Answer 1

$f(x)=6x+2,\ x_0=1\\\\f'(x_0)=\lim\limits_{h\to0}\dfrac{f(x_0+h)-f(x_0)}{h}\\\\f'(1)=\lim\limits_{h\to0}\dfrac{f(1+h)-f(1)}{h}=\lim\limits_{h\to0}\dfrac{6(1+h)+2-[6(1)+2]}{h}\\\\=\lim\limits_{h\to0}\dfrac{(6)(1)+(6)(h)-(6+2)}{h}=\lim\limits_{h\to0}\dfrac{6+6h-8}{h}\\\\=\lim\limits_{h\to0}\dfrac{6h-2}{h}=\lim\limits_{h\to0}\left(\dfrac{6h}{h}-\dfrac{2}{h}\right)=\lim\limits_{h\to0}\left(6-\dfrac{2}{h}\right)=6\\\\Answer:\ \boxed{f'(1)=6}$

Answer 2

Ich would das that the derivative of
f(x) = 6x+2
is 6
because of derivative 6x it is 6 and the derivative of 2 is 0