Help with a derivative and solving for Critical points

  • #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.
 

Answers and Replies

  • #2
SammyS
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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.
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]
 
  • #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
 
  • #4
SammyS
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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
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.)
 
  • #5
HallsofIvy
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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.
 

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