Differentiation - Quotient rule

[zebra1707]

Homework Statement

Given y = x^2 + 6 / x find x if dy/dx equals 0 zero

Homework Equations

dy/dx = v du/dx - u dv/dx / v^2

The Attempt at a Solution

I have got as far as dy/dx = x^2 - 6 / x^2

However then zero must equal Sqrt 6, which 2.44... - can someone please confirm.

Many thanks.

 

[rock.freak667]

I didn't check to see if your derivative is correct, but I will assume it is. But solving x²-6=0 yields two answers √6 and -√6 . You have two answers for x.

 

[zebra1707]

Hi Rock freak

dy/dx = x^2 - 6 all over x^2

So not sure how you arrived at x^2 - 6 = Sqrt +/- 6

Can you check my derivative calc.

Cheers

 

[rock.freak667]

Hi Rock freak

dy/dx = x^2 - 6 all over x^2

So not sure how you arrived at x^2 - 6 = Sqrt +/- 6

Can you check my derivative calc.

Cheers

Well your derivative looks correct.


$$\frac{x^2-6}{x^2}=0 \Rightarrow x^2-6=0$$

x²-a²=(x-a)(x+a). See how x= ±√6 ?