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Find equation of tangent line given only x. Please help!

  1. Feb 12, 2012 #1

    939

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    1. The problem statement, all variables and given/known data

    Find equation of tangent line, given x = -1. Not given y. I am used to having this when I am given both y and x.

    2. Relevant equations

    (x^3 - 4x + 2)(x^4 + 3x - 5)


    3. The attempt at a solution

    Differentiate
    (3x^2 - 4)(4x^3+3)

    Multiply
    12x^5 - 9x^2 - 8x^3 - 12

    Plug in -1, find slope
    12(-1)^5 - 9 (-1)^2 - 8(-1)^3 - 12
    = -5.3

    Plug in -1 to the original equation to find Y

    -35

    Find equation
    y1- = m (x1 - x2)
    y+35 = -5.3 (x+1)
    y+35 = -5.3x -5.3
    y = -5.3x - 5.3 - 35
    y = -5.3x -40.3

    ...............................

    I have a feeling this is wrong though, because I have gotten many similar questions wrong. How can I figure this out?
     
  2. jcsd
  3. Feb 12, 2012 #2

    SammyS

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    Hello 939. Welcome to PF !


    When you graph the function, (x3 - 4x + 2)(x4 + 3x - 5) , what is y ?
     
  4. Feb 12, 2012 #3

    939

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    Hi Sammy, thanks!

    When I graph it, y is -35 exactly.

    Knowing y and x, is it possible to find the equation doing:

    y-y1 = m (x-x1)
    y+35 = -5.3 (x+1)
    etc?
     
    Last edited: Feb 13, 2012
  5. Feb 13, 2012 #4

    Mark44

    Staff: Mentor

    I'm assuming that the equation is y = (x^3 - 4x + 2)(x^4 + 3x - 5)

    If y = f(x) * g(x), dy/dx [itex]\neq[/itex] f'(x) * g'(x), which is what you seem to be doing here. You should be thinking "product rule."
     
  6. Feb 13, 2012 #5

    939

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    Sorry, yes you are right about the equation. And regarding the product rule yes, you are also right!

    So, when I find it using the product rule, I insert the -1, and then that gives me the slope?
     
  7. Feb 13, 2012 #6

    939

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    So the product and then plugging in gives me 2...

    Provided I did that right, can I find the equation by doing:
    y+35 = 2(x+1)
    = 2x+2 - 35, I believe...
     
    Last edited: Feb 13, 2012
  8. Feb 13, 2012 #7

    Mark44

    Staff: Mentor

    Your arithmetic is correct, but you're being sloppy in how you present it.

    Keep your equations separated. The first equation is y+35 = 2(x+1)
    Add -35 to both sides to get a new equation y = 2x - 33
     
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