For What Value of the Constant $b$ Is There a Function $f ( x , y )$

question 6

Multiple Choice

For what value of the constant $b$ is there a function $f ( x , y )$ such that $\nabla f = b x ^ { 2 } y ^ { 2 } \mathbf { i } + x ^ { 3 } y \mathbf { j }$ ?

• A) \(0\)
• B) \(\frac { 1 } { 4 }\)
• C)\(\frac { 1 } { 2 }\)
• D)\(\frac { 3 } { 4 }\)
• E)\(1\)
• F)\(\frac { 5 } { 4 }\)
• G) \(\frac { 3 } { 2 }\)
• H)\(\frac { 7 } { 4 }\)

Compare different hypotheses explaining the indirect benefits of female mate choice.

Recognize the impact of sexual conflict on the evolution of reproductive strategies and morphology.

Analyze the strength of sexual selection among males in different species based on reproductive data.

Explain the reversal of sexual dimorphism roles in certain species and its relation to sexual selection theory.

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Definitions:

Satisfaction

The feeling of pleasure or fulfillment that comes from achieving a goal or satisfying a need.

Marginal Utility

The increase in satisfaction or utility derived from the consumption of an additional unit of a good or service.

Utility-Maximizing

A theoretical concept in economics that individuals or firms seek to achieve the greatest satisfaction or profit from their actions, subject to their resources.