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anonymous

  • 5 years ago

The function y=x^4 + bx^2 + 8x + 1 has a horizontal tangent and a point of inflection for the same value of x. What must be the value of b?

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  1. myininaya
    • 5 years ago
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    is b the y-intercept?

  2. myininaya
    • 5 years ago
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    of the tangent line?

  3. myininaya
    • 5 years ago
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    oh i see

  4. myininaya
    • 5 years ago
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    nvm i see the b lol

  5. myininaya
    • 5 years ago
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    set y'=y''

  6. anonymous
    • 5 years ago
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    Okay!

  7. myininaya
    • 5 years ago
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    i dont know if that will help us lets see what heppens

  8. myininaya
    • 5 years ago
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    oh wait erase that we have 2 equations right the one with y' and the one with y'' set both = to zero so y'' gives us 12x^2+2b=0 which means b=-12x^2/2=-6x^2 so take y' which gives us 4x^2+2bx+8=0 and where you see that x plug in -6x^2

  9. myininaya
    • 5 years ago
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    so we have 4x^3+2(-6x^2)x+8=0 4x^3-12x^3+8=0 -8x^3+8=0 and so on...

  10. myininaya
    • 5 years ago
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    you did see the typo above right when i wrote 4x^2 its suppose to be 4x^3

  11. anonymous
    • 5 years ago
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    Yea lol! I'm going to see what I get!

  12. myininaya
    • 5 years ago
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    so anyways we have 8x^3=8 so x^3=1 so x=1

  13. myininaya
    • 5 years ago
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    if x=1 and b=-6x^2, then what does b=__

  14. anonymous
    • 5 years ago
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    b=-6 and that's what the answer says!! :D

  15. myininaya
    • 5 years ago
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    did you understand the steps? do you want me to say why i did something or do you got it? this was a nice problem

  16. anonymous
    • 5 years ago
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    I understand! Yea it was a nice problem indeed!

  17. myininaya
    • 5 years ago
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    i seen another typo way up there it says replace c with -6x^2 thats suppose to be replace b with -6x^2 i cant type im sorry

  18. myininaya
    • 5 years ago
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    not c but x lol

  19. anonymous
    • 5 years ago
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    You were probably typing fast but yea I understand! Thanks!

  20. myininaya
    • 5 years ago
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    ok have funs!

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