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CalleyLeeAnn

  • one year ago

Find the derivative of f(x) = 5x + 9 at x = 2. I know this question has already been asked, but I don't understand the other answers.

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  1. CalleyLeeAnn
    • one year ago
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    Using the difference quotient, I get 0, but other sources tell me the answer is 5. How do I get the right answer using the difference quotient?

  2. misty1212
    • one year ago
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    HI!!

  3. misty1212
    • one year ago
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    for a line, derivative = slope

  4. misty1212
    • one year ago
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    we can use the :"difference quotient" if you like, it is the change in y over the change in x , which is still the slope you need the steps?

  5. CalleyLeeAnn
    • one year ago
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    Let's use the difference quotient please :) And yes, let's go over the steps because I'm obviously doing something wrong with it lol

  6. misty1212
    • one year ago
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    ok first of all, the "at x = 2" part is unnecessary because the slope of a line is a constant, and therefore does not depend on the number but since that is what it says, lets go ahead and use it are you using \[\frac{f(x)-f(a)}{x-a}\] or \[\frac{f(a+h)-f(a)}{h}\]?

  7. CalleyLeeAnn
    • one year ago
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    Number 2!

  8. misty1212
    • one year ago
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    ok so first replacing \(x\) by \(2\) we have \[\frac{f(2+h)-f(2)}{h}\]

  9. misty1212
    • one year ago
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    in this case \[f(x)=5x+9\] so \[f(2)=5\times 2+9=19\]

  10. CalleyLeeAnn
    • one year ago
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    When plugging it in isn't it supposed to look like this?:\[\frac{ (5(x+h)+9)-(5x+9) }{ h }\]

  11. misty1212
    • one year ago
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    it is if you use x instead of 2

  12. misty1212
    • one year ago
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    since it makes no difference lets do it your way

  13. CalleyLeeAnn
    • one year ago
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    Oh, okay. I didn't realize you could plug in 2 right away - I just always did it at the end

  14. misty1212
    • one year ago
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    lets do it your way anyway it is pretty easy since all you have to do is some algebra in the numerator multiply out and combine like terms

  15. misty1212
    • one year ago
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    you can almost do it in your head \[5x+5h+9-5x-9=5h\]

  16. CalleyLeeAnn
    • one year ago
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    Wow, I just realized my mistake lol.I forgot to divide by h at the end and that totally threw me off! Thanks so much for your help :D

  17. misty1212
    • one year ago
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    lol your welcome \[\color\magenta\heartsuit\]

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