Keara L.
asked • 03/05/24Use implicit differentiation to find an equation of the tangent line to the curve at the given point. y^2(y2 − 4) = x^2(x^2 − 5). (0, −2) (devils curve)
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1 Expert Answer
Mark M. answered • 03/05/24
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4.9
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Retired math prof. Calc 1, 2 and AP Calculus tutoring experience.
y4 - 4y2 = x4 - 5x2
4y3(dy/dx) - 8y(dy/dx) = 4x3 - 10x
Since (0, -2) is on the curve, -32(dy/dx) + 16(dy/dx) = 0
-16(dy/dx) = 0
So, dy/dx = 0
Equation of tangent line is y = -2.
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Dina M.
y^2 (y^2 - 4) = x^2 (x^2 - 5) y^4 - 4y^2 = x^4 - 5x^2 4y^3 y' - 8yy'=4x^3 - 10x y'(4y^3 - 8y) = 2x (2x^2 - 5) y' = x(2x^2 - 5)/(2y(y^2 - 2)) Tangent line equation y - y1 = m (x - x1) , point (x1,y1) , m = Y'(0,-2) = 0 , x1=0 , y1= -2 y + 2 = 0 , Finally, equation of the tangent line: y = -203/10/24