Question

Find the slope of the tangent line to the graph of the cissoid (3-x)y^2=x^3 at x = 2.

Answer 1

\[(3-x)y^2=x^3\quad,\quad x=2\quad\Rightarrow\quad y^2=8\quad,\quad y=\pm 2\sqrt{2}\]\[((3-x)y^2)'=(x^3)'\]\[-y^2+(3-x)2yy'=3x^2\]\[y'=\frac{3x^2+y^2}{2(3-x)y}\]\[y'(2,2\sqrt{2})=\frac{20}{4\sqrt{2}}=\frac{5}{\sqrt{2}}\]\[y'(2,-2\sqrt{2})=\frac{20}{-4\sqrt{2}}=-\frac{5}{\sqrt{2}}\]