f(x,y,z)= x(p+z)+y(p−z) +((4x^3 )/(p+z))+((4y^3 )/(p−z))+4(x+y)^2 (y−x) ∀ p(x,y)=c+(x−y)(√(1+(x+y)^2 )) +(x^2 −y^2 ) Determine x,y,z such that f is maximum. (c is a constant). Assume y≥x.


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Question Number 63015 by ajfour last updated on 27/Jun/19

$f (x, y, z) = x (p + z) + y (p - z)$ $+ \frac{4 x^{3}}{p + z} + \frac{4 y^{3}}{p - z} + 4 {(x + y)}^{2} (y - x)$ $\forall p (x, y) = c + (x - y) \sqrt{1 + {(x + y)}^{2}}$ $+ (x^{2} - y^{2})$ $D e t e r m i n e x, y, z s u c h t h a t f i s$ $m a x i m u m . (c i s a c o n s t a n t) .$ $A s s u m e y ⩾ x .$
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