Provide an appropriate response.
-Find the slope of the curve $x y ^ { 3 } - x ^ { 5 } y ^ { 2 } = - 4$ at $( - 1,2 )$.
A) $- \frac { 3 } { 4 }$
B) $\frac { 2 } { 3 }$
C) $- \frac { 3 } { 2 }$
D) $- \frac { 6 } { 5 }$

Question

Quizplus · Accepted Answer

To find the slope of the curve at a given point, we need to find the derivative $\frac{dy}{dx}$ using implicit differentiation. Differentiating both sides of the equation $x y^3 - x^5 y^2 = -4$ with respect to $x$, and then substituting the point $(-1, 2)$, we find that the slope is $-\frac{3}{2}$.

Provide an Appropriate Response xy3−x5y2=−4x y ^ { 3 } - x ^ { 5 } y ^ { 2 } = - 4xy3−x5y2=−4

Provide an Appropriate Response $x y ^ { 3 } - x ^ { 5 } y ^ { 2 } = - 4$