Homework Help

Differentiate `f(x)=x^2-5x+3` from first principle.   

user profile pic

anniepalmer | Student, Undergraduate | eNoter

Posted December 15, 2012 at 6:27 PM via web

dislike 0 like

Differentiate `f(x)=x^2-5x+3` from first principle.

 

 

1 Answer | Add Yours

user profile pic

lfryerda | High School Teacher | (Level 2) Educator

Posted December 15, 2012 at 6:39 PM (Answer #1)

dislike 1 like

To differentiate the function from first principles, we need to evaluate the limit:

`f'(x)=lim_{h->0}{f(x+h)-f(x)}/h`

Consider the numerator of the limit.

`f(x+h)-f(x)`

`=(x+h)^2-5(x+h)+3-(x^2-5x+3)`   expand brackets

`=x^2+2xh+h^2-5x-5h+3-x^2+5x-3`   collect like terms

`=2xh-5h+h^2`   factor the h

`=h(2x-5+h)`

Now put into the numerator of the limit to get:

`f'(x)=lim_{h->0}{h(2x-5+h)}/h`   cancel common factor

`=lim_{h->0}(2x-5+h)`     now take the limit

`=2x-5`

The derivative of the function is `f'(x)=2x-5` .

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes