A point moves along thex-axis with its position,x, at timetgiven by

x(t) = 2t³ 15t²+ 36t+ 5,t> 0.

Find all values oftfor which the point is moving to the right and its velocity is decreasing.

A car is moving at a constant acceleration of 3 m/sec². If the car is moving with a velocity of 20 m/sec att= 0,how fast is the car moving whent= 3?

As the second hand of a clock moves around the dial, it sweeps out a sector with a constantly increasing area.

Pablos clock has a second hand that is 5 centimeters long. How fast is the area of the sector that is swept out by the second hand increasing?

A winch on a motionless truck 6 feet above the ground is dragging a heavy load (see diagram).

If the winch pulls the cable at a constant rate of 1.5 feet/second, how quickly is the load moving on the ground when it is 11 feet from the truck?

You are an engineer working for a shipping company who is air mailing huge amounts of gasoline across the country. Your supervisor tells you that the guys upstairs in the suits want to package the gasoline in cylindrical containers that hold 10pi cubic feet of gasoline. It is your job to minimize the cost of the packaging materials. What radius should the cylinders have to minimize the amount of packaging material?

4sqrt5, 3sqrt5, sqrt5, or 5

Suppose that a certain clock has a minute hand that is 4 inches long and an hour hand that is 3 inches long. What is the rate of change of the distance between the tips of the minute and hour hands at 2:00?

Suppose a particle is moving from left to right along the graph ofy=x².Find the rate of change of the distance between the particle and the origin at the instantx= 5if the particle moves horizontally at a constant rate of 10 units/second. (In other words,dx/dt= 10)