How Do You Solve y(x+2) = 9 to Minimize x+y?

[Femme_physics]

Homework Statement

Supposed to take the derivative of:

y(x+2) = 9

I think this is one for the chain rule...


Am getting stuck with a fraction with exponent at the bottom and that's a no no that I can't get out of...

The Attempt at a Solution

Attached

 

[Pengwuino]

I'm confused, what is 'y'? And why do you change to 'f'?

 

[cristo]

You're kind of right (though I don't know why you introduce a function f). Your derivative on line 4 is off by a minus sign; it should read
$$\frac{dy}{dx}=-\frac{9}{(x+2)^2}$$

This is the solution: I don't know what you're doing in the next line.

 

[Femme_physics]

I'm confused, what is 'y'? And why do you change to 'f'?

I figured that y and f(x) are the same things just different notation.

The original question is "from all positives numbers X and Y that fulfill y(x+2) = 9, find the two numbers that for them the sum x+y is minimal."

So I thought to take the derivative of y, i.e. f(x) and set it equal to zero. Currently am stuck in the first phase though.

Edit: Oh wait, I did take the derivative successfully, just was off by a minus sign, right? :) Wheepee!

 

[Femme_physics]

You're kind of right (though I don't know why you introduce a function f). Your derivative on line 4 is off by a minus sign; it should read
$$\frac{dy}{dx}=-\frac{9}{(x+2)^2}$$

This is the solution: I don't know what you're doing in the next line.

I thought the -9 times the -1 on line 4 give a plus?

 

[diazona]

So I thought to take the derivative of y, i.e. f(x) and set it equal to zero. Currently am stuck in the first phase though.

Don't forget - what is the function that you need to minimize?

 

[Mark44]

I thought the -9 times the -1 on line 4 give a plus?

As already noted, you have an extra minus sign. In your work you have
f'(x) = -9(x + 2)^-2(-1)
That final (-1) should not be there. Your factor of -9 already includes (-1) from the exponent on x + 2.

 

[Femme_physics]

I think I completely fudged the concept of the question.

Don't forget - what is the function that you need to minimize?

The original question is "from all positives numbers X and Y that fulfill y(x+2) = 9, find the two numbers that for them the sum x+y is minimal."

That final (-1) should not be there.

Ah...thanks.. I thought that's how you use the chainrule, but you're just suppose to take the derivative of the whole thing I see. My bad.So now that I have the right derivative, but apparently my direction of how to solve the question is off because no real values = 0. I'll try to figure it out, I appreciate all the corrections with my basic calculus.