SE 4.1 1. Let \( f(x)=4-x^{2} \). Consider a rectangle with vertices \( (0,0),(x, 0),(x, y) \), and \( (0, y) \). where the vertex \( (x, y) \) lies on the curve \( y=f(x), 0 \leq x \leq 2 \) (see the picture at right). Part I . 1. Express the perimeter \( P \) of the rectangle as a function of \( x, P(x) \). 2. Find the absolute maximum and absolute minimum of \( P(x) \) on the interval \( 0 \leq x \leq 2 \). 3. Find the dimensions of the rectangle with the largest perimeter.

SE 4.1 1. Let \( f(x)=4-x^{2} \). Consider a rectangle with vertices \( (0,0),(x, 0),(x, y) \), and \( (0, y) \). where the vertex \( (x, y) \) lies on the curve \( y=f(x), 0 \leq x \leq 2 \) (see the picture at right). Part I . 1. Express the perimeter \( P \) of the rectangle as a function of \( x, P(x) \). 2. Find the absolute maximum and absolute minimum of \( P(x) \) on the interval \( 0 \leq x \leq 2 \). 3. Find the dimensions of the rectangle with the largest perimeter.

Cuál es la derivada de la siguiente función (2 puntos) * \( f(t)=e^{-2 t} \cos (4 t) ? \) \( -8 e^{-2 t} \operatorname{sen}(4 t) \) \( -2 e^{-2 t} \cos (4 t)-4 e^{-2 t} \operatorname{sen}(4 t) \) \( -2 e^{-2 t} \cos (4 t)+e^{-2 t} \operatorname{sen}(4 t) \) \( 4 e^{-2 t} \operatorname{sen}(4 t) \)

Solve the following equation in \( x \in \mathbb{R} \) : \[ 3(2 x+4)-5=3 \]

\( \frac { 2 n + n = a } { m - n - 3 } \)

Factor. \( 3 z^{2}+4 z-4 \)