At the Given Point, Find the Slope of the Curve $y ^ { 5 } + x ^ { 3 } = y ^ { 2 } + 12 x$

Multiple Choice

At the given point, find the slope of the curve, the line that is tangent to the curve, or the line that is normal to the curve,
as requested.
- $y ^ { 5 } + x ^ { 3 } = y ^ { 2 } + 12 x$ , slope at $( 0,1 )$

A) $- \frac { 7 } { 2 }$
B) $\frac { 12 } { 5 }$
C) $\frac { 12 } { 7 }$
D) 4