Question 1086904: Evaluate [f(x+h)-f(x)]/h and simplify if f(x)=2x^2 + x + 1 Found 3 solutions by Boreal, Fombitz, rothauserc:Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! f(x+h)=2(x+h)^2 +(x+h)+1=2x^2+4xh+2h^2+x+h+1
subtract from that---- -2x^2---------x---1
That is 4xh+2h^2+h
divide that by h
That is 4x+2h+1
(as h approaches 0, the expression approaches 4x+1.)
You can put this solution on YOUR website! 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
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