Posted by ibo on Wednesday, September 29, 2010 at 2:51pm.
The equation x^2 y+2xy^3=8defines y as a function of x,y=f(x), near x=2, y=1.
a) Find dy/dx.
b) Now, find the slope of the curve
x^2y+2xy^3=8 when x=2, y=1.

calculus  Reiny, Wednesday, September 29, 2010 at 4:51pm
differentiate implicitly,
x^2 + 2xy^3 = 8
2x + 2x(3y^2)dy/dx + 2(y^3) = 0
solve for dy/dx, then for b) sub in x=2, y=1
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