x2y2 – 2x = 4 – 4y, then find the slope at the point (2,-2)
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Consider the curve defined by the equation x2y2 − 2x = 4 − 4y. Use implicit differentiation to find dy and write the equation of the tangent line at the point (2,2) in dx slope-intercept form
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Ash L. asked • 27d
Consider the curve defined by the equation x2y2 − 2x = 4 − 4y. Use implicit differentiation to find dy and write the equation of the tangent line at the point (2,2) in dx slope-intercept form.
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Stephen H. answered • 27d
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(x2)(y2)-2x=4-4y ... (x2)(2ydy/dx)+(y2)(2x)-2=-4dy/dx ... dy/dx(2x2y+4)=2-2xy2
dy/dx= (2-2xy2)/( 2x2y+4) ... at P(2,2) dy/dx = (2-2*2*4)/(2*4*2+4)= -14/10
tangent line equation is ... y=mx + b where m is the slope and is equal to -14/10 found above. This y=-14/10x+b ... This line must by definition intersect with P. Using P(2,2), 2=-14/10*2+b finding b = 34/10.
Thus the tangent line is y=-14/10x +