Find and Classify the Relative Extrema and Saddle Points of the Function

question 86

Multiple Choice

Find and classify the relative extrema and saddle points of the function $f ( x , y ) = e ^ { - 2 x } \sin 4 y$ for $x \geq 0$ and $0 \leq y \leq \frac { \pi } { 2 } .$

• A) None
• B) Relative maximum \(f \left( 0 , \frac { \pi } { 8 } \right) = 1\)
• C) Saddle point \(( 0,0,0 )\)
• \(\mathrm { d } .\) Relative minimum \(f \left( 0 , \frac { \pi } { 4 } \right) = 0\)

Determine the hybridization state of carbon and nitrogen atoms in various molecules.

Recognize the molecular geometry and shapes based on VSEPR theory.

Identify and count sigma (σ) and pi (π) bonds in organic molecules.

Analyze the molecular structure to identify coplanar atoms and resonance forms.

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