Help on calc 1 homework

Question

Use implicit differentiation to find an equation of the tangent line to the curve at the given point.

x^2/3 + y^2/3 = 4

(−3√3,1)

(astroid)

Answer 1

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

(2/3) y^(-1/3) y' = (-2/3)x^(-1/3)

y^(-1/3) y' = -x^(-1/3)

y' = -x^(-1/3)/y^(-1/3)

y' = y^(1/3)/x^(1/3) = (y/x)^(1/3)

the slope is -1/3(sqrt(3)) = -sqrt(3)/9

B = y - mx

= 1 - (-sqrt(3)/9)*(3 * sqrt(3)

= 1 - -3/3 = 1 + 1 = 2

y = (-sqrt(3)/9) x + 2

Answer 2

Here is the URL to the Desmos graph referenced in the video.

https://www.desmos.com/calculator/keerdzam3m