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anonymous

  • one year ago

f(x)=6x^2+5 (f(a+h)-f(a))/h

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  1. chrisplusian
    • one year ago
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    So in this example f(x)=6x^2+5, if I told you find f(2) would you know what to do?

  2. anonymous
    • one year ago
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    yes its just plugging it in to the function

  3. chrisplusian
    • one year ago
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    You would plug 2 in everyplace there was an x. In the problem above there is an (a+h) in the argument. So every place you see an x in the original replace it with (a+h). Then the second part shows f(a) so plug a in for every instance of x.

  4. chrisplusian
    • one year ago
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    Then continue to manipulate algebraically

  5. chrisplusian
    • one year ago
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    \[f(a+h)=6(a+h)^2 +5 =6(a^2 +2ah +h^2)+5\]

  6. chrisplusian
    • one year ago
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    \[6(a^2 +2ah +h^2)+5 = 6a^2 +12ah +6h^2 +5\]

  7. anonymous
    • one year ago
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    and then subtract that from 6a^2+5?

  8. chrisplusian
    • one year ago
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    yes :)

  9. anonymous
    • one year ago
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    so i got 12ah+6h^2+10

  10. anonymous
    • one year ago
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    so divide by h?

  11. chrisplusian
    • one year ago
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    \[\frac{ 6a^2 +12ah +6h+5-(6a^2 +5) }{ h }\]

  12. chrisplusian
    • one year ago
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    \[\frac{ 12ah +6h }{ h }=\frac{ h(12a+6) }{ h }=12a+6\]

  13. chrisplusian
    • one year ago
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    Hope that helps

  14. anonymous
    • one year ago
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    im sorry but it says its wrong

  15. chrisplusian
    • one year ago
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    I see my mistake.... look up at the equation I posted just after you said "So divide by h?". In that equation I had 6h in the numerator. it should have been 6h^2. Then you would have had 12a+6h as an answer sorry about that

  16. anonymous
    • one year ago
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    ohhhh okay got it, thanks!

  17. chrisplusian
    • one year ago
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    Your welcome

  18. anonymous
    • one year ago
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    It should only be \(\huge 12a\).

  19. anonymous
    • one year ago
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    You're finding the derivative, right?

  20. anonymous
    • one year ago
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    no his answer was right

  21. anonymous
    • one year ago
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    Ok if that's what you're saying.

  22. chrisplusian
    • one year ago
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    @Maharot there is one thing missing for it to be a derivative. This was an example of the "difference of a quotient" function which represents the slope of a line secant to two points on a curve. If you wanted a derivative you are asking for the slope of that same curve but at any point. In order to do that you need to consider the "h" in the above problem as a change in the x direction and then take the limit as delta x approaches infinity. That is to say that the two points on the curve are the same and the slope represented is at a point rather than in between two points

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