For the function \( f(x)=\frac{\ln (x)}{x^{6}} \) on the interval \( [1,7] \), find the absolute extrema, as well as all values of \( x \) where they occur. Absolute maximum of \( \square \) at \( x=\square \) Absolute minimum of \( \square \) at \( x= \) (If an extremum occurs at multiple values of \( x \), enter them as a comma-separated list like \( 5,6,8 \).)

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?

valuar las siguientes i \( \int \sqrt{3-2 x} x^{2} d x \)

\( \begin{aligned} \text { 40. } y=\frac{b}{a} \sqrt{a^{2}-x^{2}} & \frac{d y}{d x} & =-\frac{b^{2} x}{d^{2} y} \\ \text { H. } y=\left(a^{2 / 3}-x^{2 / 3}\right)^{3 / 3} & \frac{d y}{d x} & =-\sqrt[3]{\frac{y}{x}}\end{aligned} \)

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

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.)