(a) \( f(x)=2400-2 x \) (b) \( A(x)=2400 x-2 x^{2} \) (c) First write the expression for the derivative used to find the \( x \) value that maximizes area. \( \frac{d A}{d x}=-4 x+2400 \) The \( x \)-value leading to the maximum area is 600 m . The maximum area of the rectangular plot is \( \square \)

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

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

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.)

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

\( 16 d ^ { 4 } y / d x ^ { 4 } + 24 d ^ { 2 } y / d x ^ { 2 } + 9 y = 0 \)