A marshy region used for agricultural drainage has become contaminated with a particular element. It has been determined that flushing the area with clean water will reduce the element for a while, but it will then begin to build up again. A biologist has found that the percent of the element in the soil \( x \) months after the flushing begins is given by the function below. When will the element be reduced to a minimum? What is the minimum percent? \( f(x)=\frac{x^{2}+16}{2 x}, 1 \leq x \leq 12 \) Find \( f^{\prime}(x) \). \( f^{\prime}(x)=\frac{1}{2}-\frac{8}{x^{2}} \) When will the element be reduced to a minimum? The element will be reduced to a minimum after 4 month(s). (Type an integer or a decimal.) What is the minimum percent of the element?

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

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.)

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

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

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