Hi, how can you find x in order to find when the derivative is equal to 0?

The answer on the answer sheet says \(x = {10\sqrt{2}}\).

Thanks for your input though, very much appreciated!

I got that x was equal to 0, obviously, but for the problem I needed the other answer which has to be positive because it's a length.

I will look into what you (Melody) did and I'll go on from there.

I assume that IS the derivate and you just want the equation solved

\(0 = {{\pi x(10(\sqrt{225-x^2}+15)-x^2})\over{\sqrt{225-x^2}}}\\ 0 =\frac{{\pi x(\sqrt{10\sqrt{225-x^2}+15)}+x)(\sqrt{10\sqrt{225-x^2}15)}-x})}{{\sqrt{225-x^2}}}\\ x=0\:\;\:or\;\;(\sqrt{10\sqrt{225-x^2}+15)}+x)=0\;\;or\;\;(\sqrt{10\sqrt{225-x^2}+15)}-x)=0\\ x=0\:\;\:or\;\;(\sqrt{10\sqrt{225-x^2}+15)}=-x\;\;or\;\;(\sqrt{10\sqrt{225-x^2}+15)}=+x\\ x=0\:\;\:or\;\;10\sqrt{225-x^2}+15=x^2\\ x=0\:\;\:or\;\;\sqrt{225-x^2}=\frac{(x^2-15)}{10}\\ x=0\:\;\:or\;\;225-x^2=\frac{(x^4-30x^2+225)}{100}\\ x=0\:\;\:or\;\;225-x^2=\frac{(x^4-30x^2+225)}{100}\\ x=0\:\;\:or\;\;22500-100x^2=x^4-30x^2+225\\ x=0\:\;\:or\;\;x^4+70x^2-22275=0\\ \)

\(x=0\:\;\:or\;\;x^4+70x^2-22275=0\\ x ^2= {-b \pm \sqrt{b^2-4ac} \over 2a}\\ x ^2= {-70 \pm \sqrt{4900+4*22275} \over 2}\\ x ^2= {-70 \pm \sqrt{94000} \over 2}\\ x ^2\approx {-70 \pm306.6 \over 2}\\ x ^2\approx {-70 \pm306.6 \over 2}\\ x ^2\approx 118.3\\ x\approx \pm10.9\\~\\ so\;I\; get\;\\~\\ x=0\;\;or\;\;x\approx \pm10.9\)

You probably should check those 2 approx answers though.   ://

Mmm I do not think it is right.  

I am not sure I am answering the right question anyway.://

x=0 is definitely a solu​tion to the question that I answered.  ://

Made the whole calc in the image thing and it got to long, which resulted in that the "ok" button went too far to the right of the screen that I was unable to click it.. New to this site.

Anyway I got the answer,

X₁ = 0 X₂ ≈ +-12,247..

Although I might aswell be wrong..

Edit: forgot the +-

We will actually end up with this equation :

pi*x (10 (sqrt(225 -x^2) + 15) - x^2)  = 0

Divide by pi*x   ....this will drop one solution of x = 0   ...and we have remaining

10(sqrt(225 - x^2) + 15) - x^2 )  = 0

10sqrt(225 - x^2) + 150 - x^2  = 0

10sqrt(225-x^2)  = x^2 - 150      square both sides

100(225-x^2) =  x^4 - 300x^2 + 22500   simplify

22500 - 100x^2 = x^4 - 300x^2 + 22500

x^4 - 200x^2  = 0      factor

x^2(x^2 - 200) = 0     obviously x = 0  is one solution [ actually, x = 0 is a multiple solution]

The other positive solution is

x^2  = 200     take the positive sq root of both sides

x = sqrt(200)   = sqrt(100 * 2)  =  10*sqrt(2) 

That is a much better answer.

Thanks Chris :)