turkey-yks 2015 Q43

turkey-yks · Other · lys1-math Stationary points and optimisation Geometric or applied optimisation problem

In the rectangular coordinate plane, the graph of the curve $y = e ^ { \left( - x ^ { 2 } \right) }$ is given.
In this plane, a rectangle with one side on the x-axis and two vertices on the curve is drawn with the maximum possible area.
What is the area of this rectangle in square units?
A) $\sqrt { \mathrm { e } }$
B) $\sqrt { 2 e }$
C) $\frac { \sqrt { e } } { 2 }$
D) $\sqrt { \frac { 2 } { \mathrm { e } } }$
E) $2 \sqrt { e }$

In the rectangular coordinate plane, the graph of the curve $y = e ^ { \left( - x ^ { 2 } \right) }$ is given.

In this plane, a rectangle with one side on the x-axis and two vertices on the curve is drawn with the maximum possible area.

What is the area of this rectangle in square units?\\
A) $\sqrt { \mathrm { e } }$\\
B) $\sqrt { 2 e }$\\
C) $\frac { \sqrt { e } } { 2 }$\\
D) $\sqrt { \frac { 2 } { \mathrm { e } } }$\\
E) $2 \sqrt { e }$

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