Find the critical points of f(x)= x sqrt(x+3). I don't know how to simplify the derivative to find the critical point. Someone help please!

Question

abb0t · Answer

Take the derivative of this function and find the roots.

abb0t · Answer

Meaning, find the zero's, and plug those values back into f(x).

anonymous · Answer

I did that but i get stuck with $$\sqrt{x+3} + \frac{ 1 }{ 2\sqrt{x+3}}$$ I don't know how to simplify it.

nincompoop · Answer

erm ...

turingtest · Answer

you forgot an x in the numerator of the second term
treat it like$$(x+3)^{1/2}+\frac12x(x+3)^{-1/2}$$which can be factored...

turingtest · Answer

$$(x+3)^{1/2}+\frac12x(x+3)^{-1/2}=(x+3)^{-1/2}(x+3+\frac x2)=0$$can you take it from here?

anonymous · Answer

I don't understand what you are doing in the 2nd part.

anonymous · Answer

Oh wait I understand it now! thank you for your help!

nincompoop · Answer

you're welcome

turingtest · Answer

Thanks nincompoop :p