Question 198110
use the definition of derivative to f'(x) when f(x)=x^2-5x+1
--------
You need to find "the limit of [f(x+h)-f(x)]/h as h goes to zero"
----------------
f(x+h) = (x+h)^2 - 5(x+h) + 1
= x^2 + 2hx + h^2 - 5x -5h +1
-----------------------------------------
f(x) = x^2 -5x +1
-----------------------------------------
So f(x+h) - f(x) = 2hx + h^2 -5h
--------------
Then, dividing by h, you get [f(x+h)-f(x)]/h = 2x + h -5
---------------------
Now take the limit as h goes to zero and you get:
f'(x) = 2x - 5
=======================
Hope that helps.
=======================
Cheers,
Stan H.