Answer to Question #234834 in Calculus for Jese Junior

Question

Use first principle method/definition method to obtain the derivative f(x) = 2 – x

Answer 1

$$f'(x)=\lim\limits_{h\to 0}\dfrac{f(x+h)-f(x)}{h}$$

$$=\lim\limits_{h\to 0}\dfrac{2-(x+h)-(2-x)}{h}$$

$$=\lim\limits_{h\to 0}\dfrac{-h}{h}=-2$$

$$f'(x)=(2-x)'=-1, x\in \R$$