How do you find the derivative of f(x)=9-1/2xf(x)=9−12x using the limit process?

1 Answer
Steve M
Nov 20, 2016

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

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