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  1. #1
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    critical point question

    Trying to figure this out, but I am totally lost.

    Question is...
    the graph of y=2x^3 - ax^2 - bx + 5 has critical points x=2 and x=-1
    find a and b

    find and identify all local extremities
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  2. #2
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    Quote Originally Posted by timmy420 View Post
    Trying to figure this out, but I am totally lost.

    Question is...
    the graph of y=2x^3 - ax^2 - bx + 5 has critical points x=2 and x=-1
    find a and b

    find and identify all local extremities
    Critical points occur at values of x such that \frac{dy}{dx} = 0. Therefore (x - 2) and (x + 1) are factors of \frac{dy}{dx} \, ....
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    should i plug in the values and then do the dx/dy of it? Im totally stumped here.
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    Quote Originally Posted by timmy420 View Post
    should i plug in the values and then do the dx/dy of it? Im totally stumped here.
    Get dy/dx.

    (x - 2) and (x + 1) are its factors.

    So dy/dx has the form A(x - 2)(x + 1).

    The coefficient of x^2 is 6 therefore A = 6.

    So dy/dx = 6(x - 2)(x + 1). Expand.

    You now have two expresions for dy/dx. Compare the expressions and hence get the value of a and b.
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    Quote Originally Posted by mr fantastic View Post
    Get dy/dx.

    (x - 2) and (x + 1) are its factors.

    So dy/dx has the form A(x - 2)(x + 1).

    The coefficient of x^2 is 6 therefore A = 6.

    So dy/dx = 6(x - 2)(x + 1). Expand.

    You now have two expresions for dy/dx. Compare then and hence get the value of a and b.
    Forget this. I have a better idea for you.

    The two solutions to dy/dx = 0 are x = 2 and x = -1. Substitute these values of x to get two equation with a and b in them. Solve the resulting equations simultaneously.
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    by subbing them into it I get

    2(2)^3-a(2)^2-b(2)+5 and 2(-1)^3 -a(-1)^2-b(-1)+5

    if I set them equal to eachother I end up with 18= 3a + 3b
    is this either bit on the right track?
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  7. #7
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    Quote Originally Posted by timmy420 View Post
    by subbing them into it I get

    2(2)^3-a(2)^2-b(2)+5 and 2(-1)^3 -a(-1)^2-b(-1)+5

    if I set them equal to eachother I end up with 18= 3a + 3b
    is this either bit on the right track?
    You're meant to substitute x = 2 and x = -1 into dy/dx = 0.

    Get two equations.

    Solve simultaneously for a and b.
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