Question

How do you use the limit definition of the derivative to find the derivative of `f(x)=-x+6`?

Answer 1

`f'(x)=-1`

Explanation:

By definition: `f'(x) = lim_"h->0" (f(x+h)-f(x))/h`

In this example `f(x)=-x+6`

Hence: `f'(x) = lim_"h->0"(-x-h+6+x-6)/h`

`f'(x) = lim_"h->0"(cancel(-x)-hcancel(+6)cancel(+x)cancel(-6))/h`

`f'(x) = lim_"h->0" -h/h =-1`