If $f ( x , y ) = x ^ { 2 } + 7 y ^ { 2 }$

question 62

Multiple Choice

If $f ( x , y ) = x ^ { 2 } + 7 y ^ { 2 }$ use the gradient vector $\nabla f ( 10,2 )$ to find the tangent line to the level curve $f ( x , y ) = 136$ at the point $( 10,2 )$ .

• A) \(10 x + 14 y = 12\)
• B) \(10 x + 14 y = 136\)
• C) \(100 x - 49 y = 12\)
• D) \(100 x + 49 y = 136\)
• E) \(100 x - 14 y = 12\)

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Definitions:

Capital Allocation Line

A line representing the risk-return trade-off of different portfolios, showing the highest expected return for a given level of risk.

Standard Deviation

A measure of the dispersion or variation in a set of values, indicating how much the values differ from the mean of the set.

Complete Portfolio

A portfolio that includes both risky assets and a risk-free asset, optimizing the balance between risk and return.