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

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

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

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

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

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

whpalmer4
 one year 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
 one year 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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