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Tangent line

  1. May 6, 2008 #1
    1. The problem statement, all variables and given/known data

    a) Graph [tex]y = -x^5 +5x -6[/tex]. Include coordinates of local max, min, and points of inflection. Indicate the behavior as x-> -infinity, x -> infinity.

    b) Find in slope-intercept form the equation of the tangent line to the curve at x = 2.

    2. Relevant equations

    3. The attempt at a solution

    a) I found that the critical numbers are 1 and -1. The POI is 0. As x->infinity the limit -> -infinity and vice versa. Coordinates are (1,-2), (0,-6), (-1,-10). I've also graphed it to match my findings.

    b) I'm not sure what to do for this part.

    Thanks for any help!
  2. jcsd
  3. May 6, 2008 #2


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    Part a) looks correct

    For part b) you just need to find the equation of the tangent to the curve at that point. So you'll need the coordinate of y at x=2 and the gradient at x=2. {gradient function=[itex]\frac{dy}{dx}[/itex]
  4. May 6, 2008 #3
    hmm.... i'm getting like 2,-13 and 2,-75? Don't think I understand what you mean...
  5. May 6, 2008 #4
    For part b) your just asked for the equation of a line that is tangent to the curve.

    Well you need a point and a slope. They give you the point: it's when x=2. Finding y' gives you the slopes at every point (btw gradient is a fancy word for slope in this case), we need the slope at x=2 because that's the point that the line needs to be tangent.
  6. May 6, 2008 #5
    so like [tex] y = -75x + -28[/tex] ?
  7. May 6, 2008 #6
    point slope form is:


    Where (x_0,y_0) is your point and m is your slope.
  8. May 6, 2008 #7


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