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Find the x coordinate of the stationary point of the following curves

  1. Nov 28, 2011 #1
    1. The problem statement, all variables and given/known data

    Find dy/dx and determine the exact x coordinate of the stationary point for:

    (a) y=(4x^2+1)^5

    (b) y=x^2/lnx

    2. Relevant equations


    3. The attempt at a solution

    (a) y=(4x^2+1)^5

    dy/dx=40x(4x^2+1)^4

    40x(4x^2+1)^4=0

    Find x... How?

    (b) y=x^2/lnx

    dy/dx=2xlnx-x^2 1/x / (lnx)^2

    2xlnx-x^2 1/x / (lnx)^2=0

    Find x... How?
     
  2. jcsd
  3. Nov 28, 2011 #2
    re 1st prob:

    Then either 40x = 0 or (4x^2+1)^4 = 0.

    and solve the above two equations.
     
  4. Nov 28, 2011 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    You are aware that [itex]x^2/x= x[/itex] aren't you?

    [itex]y= x^2/ln(x)[/itex]: [itex]y'= (2xln(x)- x)/(ln(x))^2= 0[/itex]
    Use parentheses! What you wrote was [itex]y'= 2x ln(x)- (x/(ln(x))^2)= 0[/itex].

    Multiply both sides of the equation by [itex](ln(x))^2[/itex]
    and you are left with 2x ln(x)- x= x(2ln(x)- 1)= 0. Can you solve that?
     
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