Identify the points on the curve 3 x 3 ( 4 y 2 − y 3 ) = 8 3x^3(4y^2 - y^3) = 8 where the tangent line is horizontal or vertical.

No horizontal tangent lines, vertical tangent lines at ( ± 9 3 2 4 3 , − 8 3 ) \left(\pm\frac{\sqrt[3]{9}}{2\sqrt[3]{4}},-\frac83\right) .

No horizontal tangent lines, vertical tangent lines at ( ± 9 3 2 4 3 , 8 3 ) \left(\pm\frac{\sqrt[3]{9}}{2\sqrt[3]{4}},\frac83\right) ( ± 2 3 4 <path d="M95,702 c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14 c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54 c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10 s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429 c69,-144,104.5,-217.7,106.5,-221 l0 -0 c5.3,-9.3,12,-14,20,-14 H400000v40H845.2724 s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7 c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z M834 80h400000v40h-400000z"> 3 9 <path d="M95,702 c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14 c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54 c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10 s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429 c69,-144,104.5,-217.7,106.5,-221 l0 -0 c5.3,-9.3,12,-14,20,-14 H400000v40H845.2724 s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7 c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z M834 80h400000v40h-400000z"> , 3 8 ) .

No horizontal tangent lines, vertical tangent lines at ( 8 3 , ± 9 3 2 4 3 ) \left(\frac83,\pm\frac{\sqrt[3]{9}}{2\sqrt[3]{4}}\frac{}{}\right) .

No horizontal tangent lines, vertical tangent lines at ( − 8 3 , ± 9 3 2 4 3 ) \left(-\frac83,\pm\frac{\sqrt[3]{9}}{2\sqrt[3]{4}}\frac{}{}\right) .

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4. Applications of Derivatives

Implicit Differentiation

4. Applications of Derivatives

Implicit Differentiation: Study with Video Lessons, Practice Problems & Examples

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53PRACTICE PROBLEM

Identify the points on the curve $3 x^{3} (4 y^{2} - y^{3}) = 8$ where the tangent line is horizontal or vertical.

ANSWERS OPTIONS

No horizontal tangent lines, vertical tangent lines at $\left(\pm\frac{\sqrt[3]{9}}{2\sqrt[3]{4}},\frac83\right)$ .

No horizontal tangent lines, vertical tangent lines at $(\pm \frac{\sqrt[3]{9}}{2 \sqrt[3]{4}}, - \frac{8}{3})$ .

No horizontal tangent lines, vertical tangent lines at $(\frac{8}{3}, \pm \frac{\sqrt[3]{9}}{2 \sqrt[3]{4}} \frac{}{})$ .

No horizontal tangent lines, vertical tangent lines at $(- \frac{8}{3}, \pm \frac{\sqrt[3]{9}}{2 \sqrt[3]{4}} \frac{}{})$ .

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Implicit Differentiation: Study with Video Lessons, Practice Problems & Examples

Identify the points on the curve 3x3(4y2−y3)=83x^3(4y^2 - y^3) = 8 where the tangent line is horizontal or vertical.

Identify the points on the curve $3 x^{3} (4 y^{2} - y^{3}) = 8$ where the tangent line is horizontal or vertical.