Use Implicit differentiation to find the equation of the tangent line to the curve at the given point. `y^2-2x^3=-x^4 , (1,1)`

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aruv | High School Teacher | (Level 2) Valedictorian

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We want to find tangent at point (1,1) on the curve

`y^2-2x^3=-x^4`       (i)

Differentiate (i) with respect to x ( infac implicit differentiation)




Since derivative represent slope ,so we can get slope of the tangent at (1,1)

`((dy)/(dx))_{(1,1)}=(3xx 1^2-2 xx1^2)/1`

`` `=1`

Apply point slope equation to find an equation of tangent



Thus required equation of the tangent at point (1,1) on the given curve is