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laurenn_marie7
 2 years ago
f(x)=2x^2+5x+2 ... find f(x+h)
laurenn_marie7
 2 years ago
f(x)=2x^2+5x+2 ... find f(x+h)

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Goten77
 2 years ago
Best ResponseYou've already chosen the best response.1this means whereever there is a x in the original equasion that you substituate in x+h instead

laurenn_marie7
 2 years ago
Best ResponseYou've already chosen the best response.0@Goten77 so I got to 2x^2+4xh+2h^2+5x+5h+2 ... is that as far as I can get?

Goten77
 2 years ago
Best ResponseYou've already chosen the best response.1were the directions to expand it?

laurenn_marie7
 2 years ago
Best ResponseYou've already chosen the best response.0No just to find the value

Goten77
 2 years ago
Best ResponseYou've already chosen the best response.1oh then pluggign in x+h is all ya had to do

laurenn_marie7
 2 years ago
Best ResponseYou've already chosen the best response.0oh.... so just 2(x+h)^2+5(x+h)+2 would be my answer?

whpalmer4
 2 years ago
Best ResponseYou've already chosen the best response.0That's the best you can do. You need to expand it, though. Usually this particular construct is in the context of \[\lim_{h\rightarrow0}\frac{f(x+h)f(x)}{h}\]and the subtraction of f(x) removes many of the terms and the h in the denominator cancels one or more, hopefully leaving you with a limit you can evaluate without too much pain and suffering. In the case of this problem, you would have \[\lim_{h\rightarrow0}\frac{2x^2+4xh+2h^2+5x+5h+2(2x^2+5x+2)}{h} = \]\[\lim_{h\rightarrow0}\frac{4xh+2h^2+5h}{h} =\lim_{h\rightarrow0}4x+2h+5 = 4x+5 \]

whpalmer4
 2 years ago
Best ResponseYou've already chosen the best response.0And as you'll find out soon enough, \[\frac{d}{dx}[2x^2+5x+2] = 4x+5\]

laurenn_marie7
 2 years ago
Best ResponseYou've already chosen the best response.0So confusing...so is it 4x+5 ? @whpalmer4

whpalmer4
 2 years ago
Best ResponseYou've already chosen the best response.0Sorry, that was a preview of coming attractions :) No your answer is \[2x^2+4xh+2h^2+5x+5h+2\]just like you asked about.

laurenn_marie7
 2 years ago
Best ResponseYou've already chosen the best response.0Gotcha! Thank you so much! What about for f(x)? @whpalmer4

whpalmer4
 2 years ago
Best ResponseYou've already chosen the best response.0Unless there's a part of your problem statement that you didn't include or I didn't see, f(x) isn't part of your problem, only my digression about computing derivatives...

laurenn_marie7
 2 years ago
Best ResponseYou've already chosen the best response.0No no f(x) of 2x^2+5x+2 @whpalmer4

whpalmer4
 2 years ago
Best ResponseYou've already chosen the best response.0if \(f(x) = 2x^2+5x+2\) then \(f(x) = (2x^2+5x+2) = 2x^25x2\), no?

whpalmer4
 2 years ago
Best ResponseYou've already chosen the best response.0Not to be confused with \(f(x) = 2(x)^2+5(x)+2 = 2x^25x+2\)
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