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Unit vectors and functions

  1. Jan 23, 2007 #1

    fsm

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    1. The problem statement, all variables and given/known data
    Find a unit vector that is (a) parallel to and (b) normal to the graph of f(x) at the given point. Then sketch.

    f(x)=x^2
    point=(3, 9)

    2. Relevant equations
    None that I'm aware of.


    3. The attempt at a solution
    Find parallel or perpendicular lines, planes, vectors, etc. to a given function has always been a problem for me. I never know where to start. Is it a matter of slope? If so, then how?
     
  2. jcsd
  3. Jan 23, 2007 #2

    Hootenanny

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    Okay, lets start with (a); first we must find an equation for a line parallel to the function at this point, that is the equation of the tangent at this point. How do you suppose we can do this?
     
  4. Jan 23, 2007 #3

    fsm

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    Take the derivative of the function at 2?
     
  5. Jan 23, 2007 #4

    Hootenanny

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    Close, but why at x=2?
     
  6. Jan 23, 2007 #5

    HallsofIvy

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    How about f '(x0) is the slope of the tangent line to y= f(x) at xb0, two lines are parallel if they have the same slope, and two lines are normal if the product of their slopes is -1?


     
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