Question

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

1
2
3
6

Answer 1

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

Answer 2

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