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conarroedd1

united states
Joined: Oct 9, 2009
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slope of tangent line

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how would I work the slope of the tangent line to the curve

-3x^2+1xy-2y^3=-54 at the point (-4,1)

[Oct 30, 2009 10:01:59 PM]

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pskinner

Joined: Apr 2, 2005
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Re: slope of tangent line

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how would I work the slope of the tangent line to the curve

-3x^2+1xy-2y^3=-54 at the point (-4,1)

You need to differentiate the equation, using implicit differentiation, and end up with an equation in x, y, and y'. You can then set x=-4 and y=1 and solve for y' to get the slope. So, the derivative of this equation is:

(-3)(2)x^(2-1)+x*y'+y-2(3y^(3-1)*y')=0

After substituting for x and y, you will have an equation that is linear in y', which can then be solved.
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Principal Skinner

[Oct 31, 2009 9:20:45 AM]

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