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anonymous

  • 5 years ago

Can anyone find the tangent line approximation for f(x)=x^4+3x^2, when a =-1?

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  1. myininaya
    • 5 years ago
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    f '(x)=4x^3+6x did you get this far?

  2. anonymous
    • 5 years ago
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    ok i know how you got there

  3. myininaya
    • 5 years ago
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    f '(1)=4+6=10

  4. myininaya
    • 5 years ago
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    10 is the slope of the tangent line at x=-1

  5. myininaya
    • 5 years ago
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    so we know a point on the line and we know the slope of that line and a line has form y=mx+b f(-1)=10(-1)+b we can find b now 1+3=-10+b 4=-10+b 10+4=b 14=b so the tangent line is y=10x+14

  6. anonymous
    • 5 years ago
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    For whatever reason the answers in the back of the book are telling me the tangent would equal -10x-6, is it possible we mixed signs along the way?

  7. myininaya
    • 5 years ago
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    let me do it on paper one sec

  8. myininaya
    • 5 years ago
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    is this what you are confused about? the answer in the back of the book? did you try this problem and get what I got?

  9. myininaya
    • 5 years ago
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    oh i plug in 1

  10. anonymous
    • 5 years ago
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    You didn't plug in -1

  11. myininaya
    • 5 years ago
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    right polpak

  12. anonymous
    • 5 years ago
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    No i got something like x^5+5x^4+7x^3+9x^2+6x because i thought it was F(x)=f(a)+f'(a)(x-a) inorder to solve this beast

  13. myininaya
    • 5 years ago
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    f '(-1)=-10 not 10

  14. myininaya
    • 5 years ago
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    y=-10x+b we need to know b we know a point on this line

  15. anonymous
    • 5 years ago
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    Nah, just find the slope of the tangent and plug in that slope into point slope formula

  16. anonymous
    • 5 years ago
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    Ok after you get the slope of the tangent what did you plug in to get you (x,y) values?

  17. myininaya
    • 5 years ago
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    If x=1, then y=....

  18. myininaya
    • 5 years ago
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    damn stupid 1

  19. myininaya
    • 5 years ago
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    -1

  20. anonymous
    • 5 years ago
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    \(x = -1 \implies f = x^4+3x^2 = ?\)

  21. myininaya
    • 5 years ago
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    lol

  22. anonymous
    • 5 years ago
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    thats 4 but we are stillnot jiving with the stupid books answer

  23. myininaya
    • 5 years ago
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    we are fixing to

  24. myininaya
    • 5 years ago
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    so we have y=-10x+b 4=-10(-1)+b

  25. anonymous
    • 5 years ago
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    Take the slope (-10) and the point (-1,4) and plug into point slope. \(y-y_0 = m(x-x_0)\)

  26. myininaya
    • 5 years ago
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    solve for b

  27. myininaya
    • 5 years ago
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    you can use either way

  28. anonymous
    • 5 years ago
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    Where m is the slope, \(x_0,y_0\) are the x and y for your point.

  29. myininaya
    • 5 years ago
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    b=4-10=-6 so y=-10x-6

  30. anonymous
    • 5 years ago
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    I like point slope cause I don't have to do anything else. Slope intercept is only useful if you're gonna graph it.

  31. myininaya
    • 5 years ago
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    i like slope intercept its more fun to me for some reason

  32. anonymous
    • 5 years ago
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    Ok where did we pull the y value from (4) sorry i missed how we came up with that one

  33. anonymous
    • 5 years ago
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    Plug in x=-1 to the original equation for f(x)

  34. anonymous
    • 5 years ago
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    Nevermind I'm sorry, I just figured that part out, thanks for the help guys. It has been a long day to put it nicely.

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