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iop360

  • 2 years ago

determine the values of constant real numbers a and b, so that this function is differentiable at x= -5 f(x) = (ax^2) - 4x -76 x<=(-5) = bx - 1 x > 5

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  1. iop360
    • 2 years ago
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    \[ax^2 - 4x - 76, x \le -5\] \[bx -1, x > -5\]

  2. iop360
    • 2 years ago
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    answers are a = -3 b = 26

  3. iop360
    • 2 years ago
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    what do i do to get the answers though

  4. zepdrix
    • 2 years ago
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    Hmm are you sure it's -76? Or is it suppose to be 75? I get a=-3 if its a 75.. hmm Sec ill check my work, then I can hopefully explain how i got there.

  5. iop360
    • 2 years ago
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    yes it is -76

  6. zepdrix
    • 2 years ago
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    |dw:1349558391356:dw| Here is a little example. In order for this piece-wise function be continuous, the limit from the left, needs to EQUAL, the limit from the right (approaching -5). That's why I drew those little arrows, to show that we're approaching -5 from each side. Also, their tangent line's need to be approaching the same value at that point -5. Meaning, their derivatives must be equal when approaching from the left and right. So we have a little bit of work to do. And it will give us a system of 2 equations, and we'll be able to solve for a and b from there.

  7. iop360
    • 2 years ago
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    oh ok

  8. iop360
    • 2 years ago
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    do we differentiate each equation

  9. zepdrix
    • 2 years ago
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    |dw:1349558662733:dw|

  10. zepdrix
    • 2 years ago
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    Oh i see where I made a mistake in my notes :) ok ok good this will work out fine I think.

  11. zepdrix
    • 2 years ago
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    |dw:1349558827441:dw| the -20 should be a +20 in the first picture i did.

  12. zepdrix
    • 2 years ago
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    |dw:1349558961847:dw| And from here, you have a system of equations and should be able to solve for a and b!! :) If you're stuck on how to solve the system, you can let me know.

  13. iop360
    • 2 years ago
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    so we have a choice of what equations wewant to use to solve for a and b?

  14. zepdrix
    • 2 years ago
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    Mmmm no i think we have to use both of them :)

  15. iop360
    • 2 years ago
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    oh ok

  16. zepdrix
    • 2 years ago
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    |dw:1349559254725:dw|

  17. iop360
    • 2 years ago
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    hey , i got it, thanks!

  18. zepdrix
    • 2 years ago
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    Yayyy iop \:D/

  19. iop360
    • 2 years ago
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    :D thnks for helping

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