(1) \( f(x)=x^{3}-3 x^{2}-9 x+3 \)

1) Dada la expresión para la función \( F(x) \) : \[ F(x)=\int_{-2 x}^{2 x^{2}-2 n(x)} \sin (t) d t \] encontrar \( F^{\prime}(x) \). Calcule los valores de las funciones trigonométricus usando los ángulos en radanes.

\( \int _ { 0 } ^ { 45 } \sec ^ { 4 } x d x \)

1) \( \int \sqrt{3-2 x} x^{2} d x \)

Sociologists have found that crime rates are influenced by temperature. In a town of 100,000 people, the crime rate has been approximated as \( \mathrm{C}=\frac{1}{10}(\mathrm{~T}-60)^{2}+100 \), where C is the humber of crimes per month and \( T \) is the average monthly temperature in degrees Fahrenheit. The average temperature for May was \( 72^{\circ} \) and by the end of May the temperature was rising at the rate of \( 7^{\circ} \) per month. How fast is the crime rate rising at the end of May? At the end of May, the crime rate is rising by (Simplify your answer.)

jercicio \( \mathrm{N}^{\circ} 20 \) lel vuelo ( \( \mathbf{v} \) en \( \mathrm{m} / \mathrm{hr}) \) está representado por la siguiente ecuación: \[ C=0,059 v^{2}-4,107 v+93,702 \] a) ¿A que velocidad deberá volar el ave para que el consumo de oxígeno sea mínimo? b) ¿Cuál será dicho consumo?