Exam 8: Appendix: Algebra Review

Records indicate that t hours past midnight, the temperature at the local airport was $f ( t ) = - 0.3 t ^ { 2 } + 8 t + 10$ degrees Fahrenheit. What was the average temperature at the airport between 3:00 A.M. and noon? Round your answer to one decimal place, if necessary.

Solve the given equation for x. $4 = 3 + 2 e ^ { - 7 x }$

The absolute minimum of the function $f ( x ) = 8 x ^ { 3 } - 4 x ^ { 2 } + 72 x$ on the interval 0 $\le$ x $\le$ 4 is 0.

If $f ( x ) = \left( x + 2 e ^ { - x } \right) ^ { 5 }$ , then $f ^ { \prime } ( x ) = x + 2 e ^ { - x }$

A certain nuclear power plant produces radioactive waste at the rate of 500 pounds per year. The waste decays exponentially at the rate of 1.5% per year. How many pounds of radioactive waste from the plant will be present in the long run? Round to two decimal places, if necessary.

Find the intervals of increase and decrease for the function $f ( x ) = x ^ { 2 } + 9 x - 5$

Evaluate $\int _ { 2 } ^ { \infty } \frac { 1 } { x \ln \sqrt { x } } d x$ .

Evaluate $\int e ^ { 4 x - 6 } d x$ .

Find the indicated composite function.f (5x - 4) where $f ( x ) = \frac { 1 } { x } - x$

The fraction of television sets manufactured by a certain company that are still in working condition after t years of use is approximately $f ( t ) = e ^ { - 0.2 t }$ . What fraction can be expected to fail before 4 years of use? Round your answer to two decimal places, if necessary.

Decide if the given function is continuous at the specified value of x. $f ( x ) = \left\{ \begin{array} { r l } x + 5 & \text { if } x < 2 \\3 x + 1 & \text { if } x \geq 2\end{array} ; \quad x = 2 \right.$

Find the slope (if possible) of the line that passes through the given pair of points. (17, 0) and (20, 5)

Sketch the region R and then use calculus to find the area of R. R is the region between the curve $y = x ^ { 3 }$ and the line y = 14x for x $\le$ 0.

The function y = ln 8x is concave downward everywhere.

Differentiate: $f ( x ) = x ^ { 6 } + 7$

Find the relative rate of change of f (x) with respect to x for the prescribed value x = 1.f (x) =4x³ + x² + 5

Find the points of intersection (if any) of the given pair of curves.y = 7x - 8 and y = 2x - 6

The equation of the tangent line to the curve $f ( x ) = \left( 2 x ^ { 5 } - 6 x ^ { 2 } + 6 \right) \left( x ^ { 3 } + x - 1 \right)$ at the point (0, -6) is y = 6x - 6.

Records indicate that t hours past midnight, the temperature at the local airport was $f ( t ) = - 0.3 t ^ { 2 } + 8 t + 14$ degrees Fahrenheit. What was the average temperature at the airport between 1:00 A.M. and noon? Round your answer to one decimal place, if necessary.

Find two non-negative numbers whose sum is 14 for which the product of their squares is as large as possible.