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Tangent Line at Curve

  1. Jun 13, 2013 #1
    1. The problem statement, all variables and given/known data
    Find the equation of the tangent line at the curve y= x * e^(2x) at the point (2, 2*e^(4))

    2. Relevant equations

    3. The attempt at a solution
    f'(x)= e^(2x) * (2x+ 1)
    (e^4)(5) = 5e^4
    y- 2*e^4 = 5*e^4 (x-2)
    y= 5(e^4)*x - 8*(e^4)

    Is this right? It seems too easy for me to have gotten it right :/ Thanks.
  2. jcsd
  3. Jun 13, 2013 #2


    Staff: Mentor

    To clarify, the above should be
    f'(2) = (e^4)(5) = 5e^4
    You're finding the slope of the tangent line when x = 2.
    Looks OK.
    If you understand the steps involved (find the slope of the tangent, use the point-slope form of the line), it's not very hard.
  4. Jun 13, 2013 #3
    Yes sir, that is what I got! Thank you very much.
  5. Jun 13, 2013 #4


    Staff: Mentor

    You're welcome!
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