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Math Help - Polynomial Derivative

  1. #1
    RAz
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    Polynomial Derivative

    I've answered this question but I can't get e right (I assume j'(m)*k'(m)=l'(m), but I can't make it work).

    GIVEN: j(m)=2m^2+m-6, k(m)=m^3+4

    a. Calculate j'(m) and k'(m)

    j'(m)=4m+1, k'(m)=3m^2

    b. l(m)=j(m)*k(m), work out a polynomial expression for l(m).

    l(m)=2m^5+m^4-6m^3+8m^2+4m-24

    c. Calculate l'(m)

    l'(m)=10m^4+4m^3-18m^2+16m+4

    d. Calculate j'(m)*k'(m)

    12m^2+3m

    e. What do you notice about your answers to parts c and d?

    ...

    I see no corrilation, that's why I need help. I think I didn't work out a polynomial properly? If someone could explain that'd be great.
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  2. #2
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    You aren't making a mistake. (Well, except that it should be 12m^3+3m^2.) The point of the assignment appears to be to make you recognize that the product of the derivatives is NOT equal to the derivative of the product.
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  3. #3
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    i am not sure but perhaps 3m(4m+1) may be one of the zeros of the polynomial l'(m).
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  4. #4
    RAz
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    Quote Originally Posted by drumist View Post
    You aren't making a mistake. (Well, except that it should be 12m^3+3m^2.) The point of the assignment appears to be to make you recognize that the product of the derivatives is NOT equal to the derivative of the product.
    Thanks, so a polynomial can have a power higher than four? That was my other concern.
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  5. #5
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    Quote Originally Posted by RAz View Post
    I've answered this question but I can't get e right (I assume j'(m)*k'(m)=l'(m), but I can't make it work).
    No, j'(m)*k'(m) is not the same as l'(m)

    GIVEN: j(m)=2m^2+m-6, k(m)=m^3+4

    a. Calculate j'(m) and k'(m)

    j'(m)=4m+1, k'(m)=3m^2

    b. l(m)=j(m)*k(m), work out a polynomial expression for l(m).

    l(m)=2m^5+m^4-6m^3+8m^2+4m-24

    c. Calculate l'(m)

    l'(m)=10m^4+4m^3-18m^2+16m+4

    d. Calculate j'(m)*k'(m)

    12m^2+3m
    No, you've dropped a power of m. You multiplied by 3m, not 3m^2.

    e. What do you notice about your answers to parts c and d?

    ...

    I see no corrilation, that's why I need help. I think I didn't work out a polynomial properly? If someone could explain that'd be great.
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