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Calculus help!

  1. Aug 20, 2004 #1
    On what intervals is y= l 2-x l increasing or decreasing?? Wouldnt it be its always increasing cause of the absolute symbol, but thats not the answer.

    Also find where x/(x^2) - 1 is increasing/decreasing??

    Given tan(xy)= x^2, find y'

    y' of (sinx)^x
     
  2. jcsd
  3. Aug 20, 2004 #2
    I am concern about the fact the answer to our first question is really obvious, but your two last ones are not so easy. If somebody asked you to tackle non-linear differential equations, you should be able to solve absolute value problems for a while now.
     
  4. Aug 20, 2004 #3
    Whether or not a function is positive has nothing to do with it being increasing or decreasing. Draw a graph of |2 - x|. Surely the answer will come to you.

    For the other function, study the sign of its derivative.
     
  5. Aug 20, 2004 #4
    Uh..shouldn't this be in the homework forum??

    Anyway - if my memory serves me correctly, the y = |2-x| is a "V" shaped graph - that should help you with the visualisation. I'm sure you'll figure out the rest of the problem once you draw the graph.
     
  6. Aug 20, 2004 #5
    #1 Maybe it would help you if you broke it into an inequality

    y= l 2-x l is equivalent to

    if x > 2 then y= -1*(2-x)
    if x < 2 then y = 2-x


    for #2 where is that functions critical points? i.e. where does it’s derivative = 0. Then in what intervals of the critical points is the derivative positive?


    #3 Given tan(xy)= x^2, find y'

    Ill give you a hint the derivative of the left is

    The derivative of tan(xy) multiplied by the quantity x’y + y’x

    This is implicit differentiation so you will need to solve for y’


    #4 y' of (sinx)^x

    If y = (sinx)^x
    This is chain rule.
    The outer most function is g(x) = k^x and the inner function is k(x) = sinx
     
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