if f(x)=x^2+2x-1, then f(x+h)-f(x)=

Answer 1

f(x+h) = (x+h)^2 + 2 (x+h) - 1
= x^2 + 2 h x + h^2 + 2 x + 2 h - 1
now subtract x^2 + 2 x - 1
-----------------------------------
2 h x + h^2 + 2 h

Now note
if you divide that by h you get 2 x + h + 2
then let h -->0
you get 2 x + 2
therefore the limit as h---> =0 of the slope of the function is 2 x + 2
Next week you will call that the "derivative" of that function