Question

Find the slope of the function -2x + 1 by the definition of limit.

a0

Answer 1

Let
`f(x)=-2x+1`. By definition, the derivative is

`f'(x)=\displaystyle\lim_(h\to0)\frac{f(x+h)-f(x)}h`

So

`f'(x)=\displaystyle\lim_(h\to0)\frac{(-2(x+h)+1)-(-2x+1)}h=\lim_(h\to0)\frac{-2h}h=\lim_(h\to0)-2=-2`

and the slope of any line tangent to
`f(x)` is -2.