anonymous
  • anonymous
I have no idea how to solve this. Can someone please help me for a medal? :) (posting below)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
\[\frac{ f(x+Δx)−f(x) }{ Δx }\] if f(x) = x^2
IrishBoy123
  • IrishBoy123
compute as \(\huge \frac{(x + \Delta x)^2 - x^2}{\Delta x}\)
IrishBoy123
  • IrishBoy123
so expand out the \(\large (x + \Delta x)^2\) in the numerator :p

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More answers

anonymous
  • anonymous
I know how to get to the expanding part, but I am not sure how to expand the numerator. Could you show me how?
anonymous
  • anonymous
Would it end up looking like this... \[\frac{ x^{2} + Δx^{2}-x^{2} }{ Δx } \]
IrishBoy123
  • IrishBoy123
first expand out \( (x+Δx)^2\) on its own that's \( (x+Δx) \times (x+Δx)\)
IrishBoy123
  • IrishBoy123
|dw:1440705634106:dw|
anonymous
  • anonymous
That makes sense, but how do you multiple an "Δx" by an "x"
IrishBoy123
  • IrishBoy123
\(x \times \Delta x = x \ \Delta x\)
anonymous
  • anonymous
So the numerator would end up being... \[\frac{ x^{2}+2xΔx+Δx^{2}-x^{2} }{ Δx }\] which would simplify to... \[\frac{ 2xΔx+Δx^{2} }{ Δx }\] is that correct?
IrishBoy123
  • IrishBoy123
\[\checkmark\]
IrishBoy123
  • IrishBoy123
now finish it!
anonymous
  • anonymous
\[\frac{ Δx(2x+Δx) }{ Δx }\] And the final answer would be... 2x+Δx ?
IrishBoy123
  • IrishBoy123
yay! well done learning calculus? happy days!
anonymous
  • anonymous
Thank you so much. :)
IrishBoy123
  • IrishBoy123
any time! thank you.

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