[This "forum" is closed but if you want to say something, then by all means, go ahead ;-)]
Hey guys! This is not an update or a sequel (one which I know I should be doing on my other stories). I just want to see if any of you can help me. Haha. A little weird poll on how many people sees this page. Its an Add Maths question I can't do. Haha....just for a little fun. Its Differentiation. I'm studying for this major (I mean, MAJOR) exam currently so yeah...All you smart people, I know you have some brain juice for me! Haha :-)
Given that xy² = 32, find the possible values of x and of y that make L = x + y a minimum.
Can any of you do this?
Thank you guys! I know its weird but yeah...just put your answer down there in the comment box! (Plus working if can)
Thanks!
poohbear98
PS: Do you guys like questions like this? I can drop them at the end of some chapters in my future stories...just for fun's sake. Maybe a riddle or a nerd-question. Haha. No google-ing for answers.
PPS: First answer from @LieselRidges in the media box. It's not the correct method but correct answer. Eye opener for me. She made it so simple! Go her!
UPDATE: The Answer
xy² = 32
x = 32/y² ----1
L = x + y -----2
Substitute 1 into 2
L = (32/y²) + y
= 32y-2 + y
dL/dy = -64y^-3 + 1
= -64/y^3 + 1
When L is minimum,
dL/dy = 0,
-64/y^3 + 1 = 0
64/y^3 = 1
y^3= 64
y = 4
Substitute x = 4 into xy² = 32
When y = 4,
x(4)² = 32
x = 32/16
= 2
d²L/dy² = 192/4^4
= 192/256
= 0.75
d²L/dy² > 0
>> L is minimum when y = 4
[ L is minimum when x = 2 and y = 4 ]
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