SOLUTION: a curve (dy/dx) = x^1/2-x^-1/2 the curve passes through point (4,2/3) •find the equation of the curve •find (d^2y/dx^2) •find stationary points and determine its nature

Algebra ->  Trigonometry-basics -> SOLUTION: a curve (dy/dx) = x^1/2-x^-1/2 the curve passes through point (4,2/3) •find the equation of the curve •find (d^2y/dx^2) •find stationary points and determine its nature      Log On


   



Question 934068: a curve (dy/dx) = x^1/2-x^-1/2 the curve passes through point (4,2/3)
•find the equation of the curve
•find (d^2y/dx^2)
•find stationary points and determine its nature

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Integrate,
dy%2Fdx=x%5E%281%2F2%29-x%5E%28-1%2F2%29
y=%282%2F3%29x%5E%283%2F2%29%2B2x%5E%281%2F2%29%2BC
Use the point to solve for C
2%2F3=%282%2F3%294%5E%283%2F2%29%2B2%2A4%5E%281%2F2%29%2BC
2%2F3=%282%2F3%298%2B4%2BC
C=-26%2F3
highlight%28y=%282%2F3%29x%5E%283%2F2%29%2B2x%5E%281%2F2%29-26%2F3%29
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d%28dy%2Fdx%29%2Fdx=%281%2F2%29x%5E%28-1%2F2%29%2B%281%2F2%29x%5E%28-3%2F2%29
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