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Same calculus question thats been floating around for over a week...?
Plz just help in anyway you can. I'm not purposely being lazy, I, and many others in my class, are completely lost. the best I can figure is just set the rest of the variables to 1?...but in other problems, like ones involving Poiseuille's law, the of r tuns to 0...which would make 5. equal zero. PLEASE PLEASE PLEASE help us!
5. Research indicates that the power P required by a bird to maintain flight is given by the formula
P(v) = w^2/2pSv + 1/2 p A v^3
where v is the relative speed of the bird, w is its weight, p is the density of the air, and S and A are constants associated with bird’s size and shape. What speed will minimize the power expended by the bird? Assume that w, p , S, and A are positive constants.
1 week ago
6. The production of blood cells plays an important role in medical research involving leukemia and other so-called dynamical diseases. In 1977, a mathematical model was developed by A. Lasota that involved the cell production function
P(x) = Ax^s e^(-sx/r)
where A, s, and r are positive constants and x is the number of granulocytes (a type of white blood cell) present. Find the granulocyte level x that maximizes the production function P. How do you know it is a maximum?
1 Answer
- kbLv 77 years agoFavorite Answer
5) Do you mean P(v) = w^2/(2 p S v) + (1/2) p A v^3
or P(v) = (w^2/(2 p S)) v + (1/2) p A v^3
**Please clarify the placement of the parentheses so I can answer this properly.
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6) P'(x) = Asx^(s-1) * e^(-sx/r) + Ax^s * (-s/r)e^(-sx/r)
............= As e^(-sx/r) x^(s-1) [1 - (x/r)s], by factoring
Setting P'(x) = 0 yields 1 - (x/r)s = 0 ==> x = s/r. (We ignore x = 0.)
Since P'(x) > 0 for x < s/r (try x = (1/2)(s/r)), and P'(x) < 0 for x > s/r (try x = 2s/r),
we conclude that x = s/r yields a maximum.
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I hope this helps!
