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Answer Check - Find an equation of the tangent line

  1. Jul 10, 2008 #1
    1. The problem statement, all variables and given/known data
    Find an equation of the tangent line to the curve y = 5x3 at the point

    (-3,-135). Enter your equation in y = form.

    2. Relevant equations


    3. The attempt at a solution

    Taking the derivative of the equation I get

    y = 15x2, following that I plug in the x value of the given point:
    y = 15(-3)2
    and get
    y = 135

    Am I doing this correctly?
     
  2. jcsd
  3. Jul 10, 2008 #2

    quasar987

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    Science Advisor
    Homework Helper
    Gold Member

    First, you should write the derivative of y with a different symbol than "y". Conventional notations for the derivative are y' or dy/dx.

    So you have found

    y'(x) = 15x² ==> y'(-3)=135,

    which is correct. But y'(3) represents the slope of the curve y(x) at the point (-3,-135). You are asked to find an equation for the line of slope 135 and passing through the point (-3,-135).
     
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