s=(√(a^2 +(a^2 −d)^2 ))+(√((b−a)^2 +(b^2 −a^2 )^2 )) +(√(b^2 +(c−b^2 )^2 ))+c−d p= a(a^2 −d)+(a+b)(b^2 −a^2 ) +b(c−b^2 ) Find a,b,c, or d in terms of s if p is maximum. Assume a,b,c,d ≥0 .


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Question Number 63090 by ajfour last updated on 28/Jun/19

$s = \sqrt{a^{2} + {(a^{2} - d)}^{2}} + \sqrt{{(b - a)}^{2} + {(b^{2} - a^{2})}^{2}}$ $+ \sqrt{b^{2} + {(c - b^{2})}^{2}} + c - d$ $p = a (a^{2} - d) + (a + b) (b^{2} - a^{2})$ $+ b (c - b^{2})$ $F i n d a, b, c, o r d i n t e r m s o f s$ $i f p i s m a x i m u m .$ $A s s u m e a, b, c, d ⩾ 0 .$
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