Ask me
- Locked due to inactivity on Aug 4, '16 4:27pm
Thread Topic: Ask me
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happypuppy NewbieAsk a way
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Tell me the least obvious reason in still awake
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why is pinkie pie so frickin' cute?
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why do i feel attracted to short girls? what is your name? tell me tell me tell me!!!
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Determine the regions of the pq-plane for which the function f(x,y) = 2px + qy^2 restricted to the curve x^3 + y^3 = 1 has exactly one and exactly three critical points, respectively.
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happypuppy NewbieOk im emilee and thats your thoughts k
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F(x,y,k)=2px+qy^2+k(x^3+y^3-1)
Fx=2p+2kx^2=0
Fy= 2qy+3ky^2=0
so y=0 and x=1
2q+3ky=0 so k=-2q/3y=-2p/3x^2
q/y=p/x^2 so y=qx^2/p and (q/p)^3x*x^6+x^3-1=0
call x^3=z
(p/q)^3z^2+z-1=0 if 1+4(p/q)^3>0 there are two roots for x^3 and so for x and added to (1,0) there are three critical points
If 1+4(p/q)^3=0 (p/q)^3=-1/4 and -1/4z^2+z-1=z^2-4z+4=(z-2)^2=0 and z=2 and x=2^1/3
if 1+(p/q)^3 < 0 only one critical point (1,0)
I can solve my own problems.
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