At the Given Point, Find the Slope of the Curve $x ^ { 6 } y ^ { 6 } = 64$

question 59

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.
- $x ^ { 6 } y ^ { 6 } = 64$ , normal at $( 2,1 )$

• A) \(y = 2 x - 3\)
• B) \(y = - \frac { 1 } { 2 } x + 2\)
• C) \(y = \frac { 1 } { 32 } x\)
• D) \(y = - 2 x + 5\)

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Definitions:

Stones

Hard, solid masses that can form in different parts of the body, such as the kidneys (kidney stones) or gallbladder (gallstones), often causing pain.

Salivary Gland

Glands located in and around the mouth and throat that produce saliva, which aids in digestion and keeps the mouth moist.

Choledolithotomy

A surgical procedure to remove gallstones from the bile ducts or gallbladder.

Stones Removal

A medical procedure aimed at eliminating kidney or gallbladder stones.