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Derivatives: Logarithmic Function help

  1. Oct 14, 2009 #1
    1. The problem statement, all variables and given/known data
    Find an equation of the tangent line to the curve
    [tex]$\displaystyle \Large y = (2 x^2+5 )\ln (4 x^2-3 )+7$[/tex]
    when x = 1.


    2. Relevant equations
    [tex]$\displaystyle \Large y = f'(x_0)(x-x_0)+f(x_0).$[/tex]


    3. The attempt at a solution
    the fact that the tangent line to the curve y = f(x) when x = a is given by
    [tex]$\displaystyle \Large y = f'(x_0)(x-x_0)+f(x_0).$[/tex] and a=1

    f(1) = 7
    f'(1) = 48
    tangent line => y=48x-41
    right?

    this is how i did it:
    f(1) = 7 (just plug in the number in f(x)
    for f'(1),
    i did:
    [tex]$\displaystyle \Large dy/dx = 4x\ln (4 x^2-3 )+(1/(4 x^2-3 ) )* 8x * (2 x^2+5 )$[/tex]
    and pluged in 1 and got 48.

    then found the tangent line by doing y=mx+b ==> y=48x+b ==> 7=48*1+b ==> b= -41
    y=48x-41

    is everything correct so far?
     
  2. jcsd
  3. Oct 14, 2009 #2

    Mark44

    Staff: Mentor

    Everything looks fine, but I didn't check all of your arithmetic. Your value for f(1) is correct and your derivative is correct, but I didn't confirm it for f'(1).
     
  4. Oct 14, 2009 #3
    I get another number for f'(1), not 48.
     
  5. Oct 15, 2009 #4
    omg.. what a stupid mistake... bhahaha, its 56 actually..
    kk i got it lol.
    thanks!
     
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