NourShaikh
New member
- Joined
- Nov 16, 2013
- Messages
- 4
I am required to show that x²y²(4-x)²(4-y)²<=16<=16 for all #'s X and Y such that absvalue(x)<=2 and absvalue(y)<=2.
Firstly, I combined variables:
(4x²-x^4)(4y²-y^4)<=16
Then I tried writing it as such:
(4x²-x^4)(4y²-y^4)<= 4*4 = 16
Then I tried to isolate x. It appears to me that this is a maximum problem and I need to differentiate each portion.
If my f(x) = (4x²-x^4), than f'(x) = -4x³+8x.
I set f'(x)=0 and I get -4x(x²-2) so x=0 and plus/minus √(2).
When I plug 0, -√2 and +√2 back in for x to find there F(x) values, I find that f(0)=0 while f(√2) leaves me with:
16y²-4y^4-16
foil = -4(y²-2)² therefore y= plus/minus √(2)
I'm not sure if I'm in the right direction. Is my approach correct in breaking down the 16 and looking for the f'(x) = 0 to find that the max doesn't exceed 2 or -2? Or should I be using implicit differentiation which seems quite tedious?
Firstly, I combined variables:
(4x²-x^4)(4y²-y^4)<=16
Then I tried writing it as such:
(4x²-x^4)(4y²-y^4)<= 4*4 = 16
Then I tried to isolate x. It appears to me that this is a maximum problem and I need to differentiate each portion.
If my f(x) = (4x²-x^4), than f'(x) = -4x³+8x.
I set f'(x)=0 and I get -4x(x²-2) so x=0 and plus/minus √(2).
When I plug 0, -√2 and +√2 back in for x to find there F(x) values, I find that f(0)=0 while f(√2) leaves me with:
16y²-4y^4-16
foil = -4(y²-2)² therefore y= plus/minus √(2)
I'm not sure if I'm in the right direction. Is my approach correct in breaking down the 16 and looking for the f'(x) = 0 to find that the max doesn't exceed 2 or -2? Or should I be using implicit differentiation which seems quite tedious?
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