Question

How do you find the derivative of `f(x)=9-1/2x` using the limit process?

Answer 1

`f'(x)=-1/2`

Explanation:

By definition of the derivative `f'(x)=lim_(h rarr 0) ( f(x+h)-f(x) ) / h`
So with `f(x) = 9 - 1/2x` we have;

`f'(x)=lim_(h rarr 0) ( { 9-1/2(x+h)} - { 9-1/2x} ) / h`
`:. f'(x)=lim_(h rarr 0) ( 9-1/2x-1/2h - 9+1/2x ) / h`
`:. f'(x)=lim_(h rarr 0) ( -1/2h ) / h`
`:. f'(x)=lim_(h rarr 0) -1/2`
`:. f'(x)=-1/2`