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Derivative question

  1. Mar 10, 2010 #1
    1. The problem statement, all variables and given/known data


    when you are finding the slope of a fuction at a point, you are finding the slope of that point with respect to what?

    I dont understand how the square root function at point x = 4 slope is 1/4 shouldnt its slope be 1/2. please explain
    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 10, 2010 #2

    berkeman

    User Avatar

    Staff: Mentor

    Slope is defined as rise/run, or delta_y/delta_x.

    How do you mathematically find the slope of the function SQRT(x) at any given point? Show us the math of taking the derivative of SQRT(x) and plug in x=4. What answer do you get? (Please show your work)
     
  4. Mar 10, 2010 #3

    Mark44

    Staff: Mentor

    Let f(x) = x1/2
    Then f'(x) = (1/2)/x1/2
    f'(4) = ?

    The slope is relative to the horizontal axis.
     
  5. Mar 10, 2010 #4
    Thank you Berkeman and Mark. I was making a silly mistake in assuming that a slope of a curve is costant throught the entire function. I researched on the difinition the derivative and it made me understand that 1/4 is not the slope of the entire curve, 1/4 is just the slope of a single point on the curve. Thanks again for the replies.
     
  6. Mar 10, 2010 #5

    Mark44

    Staff: Mentor

    More precisely, the 1/4 is the slope of the tangent line to the curve at a single point on the curve. It doesn't make sense to talk about the slope of a point.
     
  7. Mar 11, 2010 #6
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