If $f ( x , y ) = x ^ { 2 } + 9 y ^ { 2 }$

question 136

Multiple Choice

If $f ( x , y ) = x ^ { 2 } + 9 y ^ { 2 }$ , use the gradient vector $\nabla f ( 10,2 )$ to find the tangent line to the level curve $f ( x , y ) = 136$ at the point $( 10,2 )$ . Select the correct answer.

• A) \(100 x + 81 y = 136\)
• B) \(100 x - 136 y = 12\)
• C) \(10 x + 18 y = 136\)
• D) \(100 x - 18 y = 12\)
• E) \(10 x + 18 y = 12\)

---

Definitions:

Reserves

Areas designated for the preservation of wildlife, natural resources, or cultural heritage, with restrictions on development and use.

Natural Gas

A fossil fuel consisting primarily of methane, used as an energy source for heating, cooking, and electricity generation.

Methane

A colorless, odorless flammable gas that is the simplest alkane and a major component of natural gas, contributing significantly to the greenhouse effect.

Net Useful Energy Yield

The amount of energy that remains available for use after subtracting the energy expended in obtaining and converting it.