1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Function Question

  1. Apr 30, 2007 #1
    1. The problem statement, all variables and given/known data

    If f(x)=| log x | , then state whether the following are true or false :
    a)y'(1+) =1/x
    b)y'(1)=1
    c)y'(0)= ∞ (infinity)


    2. Relevant equations

    |y| = y if y >=0
    |y| = -y if y<0


    3. The attempt at a solution

    a)The first one is true because if x > 1, then y > 0 and | y | is y. So, y' = 1/x

    b)If x=1, y=0 and so |y| = y . So y' =1/x = 1

    c)If x=0, y is not defined ?

    I am having trouble with b) and c) . I dont understand whether to check by putting values first (which would give all constant, and IMO is wrong) or later as I have done.
    The answers are T,F,F

    Any help is appreciated
     
  2. jcsd
  3. Apr 30, 2007 #2

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    For part b, (I'm assuming y=f), y'(x) exists if y'(x+) = y'(x-) (this is for a particular x). So you need to show the derivative from the left = the derivative from the right (or show it doesn't)

    Otherwise, for example, let y=|x|. y(0) = 0, so y'(0) = x' = 1. But this is clearly false.

    For part c, I'm tempted to guess they want y'(x) as x->0 from above (otherwise you're absolutely correct). This is actually negative infinity (it cna be seen just by graphing y), so it's false either way.
     
  4. Apr 30, 2007 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Office shredder made a good try but what you've written makes very little sense. For one thing you say that f(x)= |log x| but then never mention f again! Is y = f?

    "y'(1+)= 1/x" What does "1+" mean? OfficeShreder interpreted it to mean the "right derivative" or "limit from the right" but if that were correct and you are asking for the derivative as you approach x= 1 from the right, then there would be no "x" in the derivative.

    If x> 1 then f(x)= log x. What is the derivative of that? What is the limit of the derivative as x-> 1 from above? If x< 1, then f(x)= - log(x). What is the derivative of that? What is the limit of that as x-> -1 from below?

    Yes, you are correct that f(0) is not defined and neither is f'(0). I personally don't like saying that something is infinity when it is not defined! However, here, I think you need to look at what happens to |log x| and its derivative for numbers like x= 0.0001, x= 0.00000001, etc.
     
  5. May 1, 2007 #4
    Thx OfficeShredder and Halls for the help.

    sorry about the ambiguity but I cant help, I just copied all that's there in in the text. I rechecked but i see no corrections to make. I s'pose 1+ to mean Numbers greater than one. And about y being f, i think its true else the question doesnt make sense to me.

    LHL is not equal to RHL, so is the function not differentiable at x=1?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Function Question
  1. Function questions (Replies: 2)

Loading...