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Math Help - Have no idea what to do..

  1. #1
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    Have no idea what to do..

    If the function f(x) is differentiable and

    f(x)=
    {ax^3 + 6x, if x≤1
    { bx^2 + 4, if x>1

    then a =

    What do I do?? No idea what's going on..
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by elpermic View Post
    If the function f(x) is differentiable and

    f(x)=
    {ax^3 + 6x, if x≤1
    { bx^2 + 4, if x>1

    then a =

    What do I do?? No idea what's going on..
    You need to do two things.

    First, in order for it to be differentiable, it must be continuous at that point.

    So you want to see where \lim_{x\to1^-}f\left(x\right)=\lim_{x\to1^+}f\left(x\right).

    Then. For it to be differentiable at that point, the slopes of the two piecewise functions must be the same at that point. This means that 3a+6=2b

    You will then be able to come up with a system of equations. Now you can solve it for a.

    Does this make sense? Can you take it from here?
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  3. #3
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    I got my answer as b=4, a=2

    I don't think it is right however..
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by elpermic View Post
    I got my answer as b=4, a=2

    I don't think it is right however..
    I got a=-2 and b=0.

    What did you get for your system of equations?
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  5. #5
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    Quote Originally Posted by elpermic View Post
    I got my answer as b=4, a=2

    I don't think it is right however..
    why don't you?
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  6. #6
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    a-b=-2
    a-2b=-6
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  7. #7
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    Quote Originally Posted by skeeter View Post
    why don't you?

    These were the choicces..

    a)0
    b)1
    c)-14
    d)-24
    e)26
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  8. #8
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    I get a = -2 also ... recheck the original function, make sure you copied it down correctly.
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  9. #9
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    Double checked, it is the same exact function as it says on my paper..

    Don't know what's up with this one..
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