Math $201$ Communication Hoasework Probless $13$

Bailey

$13.$ Consider the curve given by the equation $2x^3-7xy{y}^3=1,$ and note that the point $(2,7)$ lies on this curve.

$($a$)$ Use Implict diferentation to find a formuls for $\frac{dy}{dx}$ the trebere rady.

$($b$)$ Find the exact slope of the tangent line to the curve determined by $2x^3-7xy{y}^3=1$ at the point $(2,3).$

$($c$)$ Find the equation of the tangent line to the curve determinad by $2x^3-7xy{y}^3=1$ at be point $(2,3).$