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Homework Help: Find the gradient of the tangent

  1. Mar 18, 2010 #1
    1. The problem statement, all variables and given/known data


    For every x>-4 where x[tex]\in[/tex] [tex]\Re[/tex] applies

    sinx+x[tex]\leq[/tex]f(x)[tex]\leq[/tex]8[tex]\sqrt{x+4}[/tex]-16

    Find the gradient of the tangent to the curve of f at x[tex]_{0}[/tex]=0

    Please help me I am trying to solve this exercise for more than two hours!
    I'm desperate.
     
  2. jcsd
  3. Apr 29, 2010 #2
    i think the functions is g(x) <=f(x)<=h(x) has
    slope [g(x) at x=0 ] = 2 and
    slope [h(x) at x=0 ] = -2
    however i think the function is too many in between so the question is not relevant [ i think].
     
  4. Apr 29, 2010 #3

    HallsofIvy

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    Science Advisor

    No, [itex]h(x)= 8\sqrt{x+ 4}- 16= 8(x+4)^{1/2}- 16[/itex]
    so [itex]h'(x)= 4(x+ 4)^{-1/2}[/itex] and h'(0)= 4/2= 2, not -2.

     
  5. Apr 30, 2010 #4
    i think you should recheck your answer,please see h'(0) = -2:smile:
     
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