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)`

1 Answer | Add Yours

aruv's profile pic

aruv | High School Teacher | (Level 2) Valedictorian

Posted on

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



We’ve answered 319,823 questions. We can answer yours, too.

Ask a question