Question 1086904
we are asked for the first derivative of f(x) = 2x^2 +x +1
:
Note that f'(x) = 4x +1
:
f(x+h) = 2(x+h)^2 + (x+h) + 1
f(x+h) = 2(x^2 +2xh +h^2) +(x+h) +1
f(x+h) = 2x^2 +4xh +2h^2 +(x+h) +1
:
(2x^2 +4xh +2h^2 +x +h +1 - 2x^2 -x -1) / h
(4xh +2h^2 +h) / h
4x +2h +1
:
as h approaches 0, we have
:
4x +1
: