Find the x-coordinate of the stationary point of the curve ,

What I did

Stationary Point, dy/dx=0

however question states x>0 and ans is 1!

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- Sep 14th 2010, 12:31 AMPunchFind x-coordinate of stationary point
Find the x-coordinate of the stationary point of the curve ,

__What I did__

Stationary Point, dy/dx=0

however question states x>0 and ans is 1! - Sep 14th 2010, 12:46 AMMathoMan
You've made a mistake when you divided the expression with the term .

This is what you should do:

And now you see that the equality will hold if either or , that is if or Since you have a constraint the correct answer is - Sep 14th 2010, 12:47 AMPunch
Thank you! but why was that a mistake?

- Sep 14th 2010, 01:13 AMMathoMan
Because you cannot be sure whether or not you carried out a division by zero! For an example, if you want to divide something with an expression (x-1) than you should point out that you exclude the possibility of x taking the value 1, thus you

*loose*a possible solution, which exactly was the case here. And I suspect that wast the idea of the given problem, to see if one is aware of what I just said in the first two sentences of this post. - Sep 14th 2010, 04:24 AMHallsofIvy
As Mathoman said, you cannot divide by 0. What you could have done, rather than factor, was, at the point where you had

was think "**If**x- 1 is**not**0, I can divide both sides by to get 3(x+ 1)= x- 1, 3x+ 3= x- 1, 2x= -4, x= -2. But**if**x- 1= 0, then both sides would equal 0 so x= 1 is also a solution."

If the condition "x> 0" had not been included, both x= -2 and x= 1 would have given stationary points. With that condition, only x= 1 does.