Question

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

Answer 1

$f'(x_0)=\lim\limits_{x\to x_0}\dfrac{f(x)-f(x_0)}{x-x_0}\\\\f(x)=6x+2;\ x_0=1\\\\f'(1)=\lim\limits_{x\to x_0}\dfrac{(6x+2)-(6\cdot1+2)}{x-1}=\lim\limits_{x\to x_0}\dfrac{6x+2-8}{x-1}\\\\=\lim\limits_{x\to x_0}\dfrac{6x-6}{x-1}=\lim\limits_{x\to x_0}\dfrac{6(x-1)}{x-1}=\lim\limits_{x\to x_0}6=6\\\\\\Answer:\boxed{f'(1)=6}$

Answer 2

Answer:

6

Step-by-step explanation:

Looking for the derivative of a function is similar to differentiating the function.

Given the function f(x) = 6x+2

The derivative of the function

f'(x) = 6

The derivative of the function at x= 1 will still be equivalent to 6 since 6 is just a constant.