1. Limited time only! Sign up for a free 30min personal 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!

Help with a derivative and solving for Critical points

  1. Jun 21, 2012 #1
    I have the equation

    (x^2)/(sqrt(x+1))

    This one has been stumping me, not sure how to reduce the derivative properly much less solve for 0.

    I get it down to this using the quotient rule:

    ((x+1)^(1/2)*2x - x^2*1/2(x+1)^(-1/2)) / (x+1)

    Just started learning derivative a few weeks ago and they're still stumping me. I'm really terrible at simplifying these down. Once it's simplified down how would I solve for ZERO to find the crit points?

    Any help would be appreciated.
     
  2. jcsd
  3. Jun 21, 2012 #2

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Hello LLofantaine. Welcome to PF !

    The derivative is correct. The rest is just algebra.

    ((x+1)^(1/2)*2x - x^2*1/2(x+1)^(-1/2)) / (x+1) → [itex]\displaystyle \frac{2x\sqrt{x+1}-\displaystyle \frac{x^2}{2\sqrt{x+1}}}{x+1}[/itex]
     
  4. Jun 21, 2012 #3
    Thanks, so that's what the derivative looks like, is there anyway to simplify that down further? Also, my algebra skills are obviously horrible so I can't remember the first thing about setting and solving that for 0
     
  5. Jun 21, 2012 #4

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    To reduce the fraction, multiply the "main" numerator & denominator by √(x+1) . That should allow you to simplify the numerator greatly.

    (Yes. When students say they're having trouble doing the calculus, it's often the algebra skills that are lacking.)
     
  6. Jun 22, 2012 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    The simplest way to handle this is NOT to use the quotient rule but, instead, write it as [tex]x^2(x+ 1)^{-1/2}[/tex] and use the product rule.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook