Teacher/User Name: DEMO Name:__________________________ Practice Problems Period: ________ Date: ____________

### Solve:

1) The perimeter of a rectangle is 21 cm. This means the area of the rectangle can be given with the formula A(x) = x(10.5 - x).
Find the maximum area of the box.

2) An object thrown straight up has a height given by: s = -16t2 + vot + so. Where s = the height at time t seconds, vo is the velocity, and so is the initial height of the object. Suppose an object is thrown upwards from the top of a tower 40 feet high with an initial velocity of 70 ft/sec.
Find the maximum height of the object.
3) An open box is to be made from a square piece of cardboard 11 cm on each side by cutting equal squares with sides of length x from the corners and turning up the sides.

The volume of the box is given by the function: V(x) = x (11 - 2x)2. Find the domain of V(x).

4) An object thrown straight up has a height given by: s = -16t2 + vot + so. Where s = the height at time t seconds, vo is the velocity, and so is the initial height of the object. Suppose an object is thrown upwards from the top of a tower 220 feet high with an initial velocity of 100 ft/sec.
Find the number of seconds until the object hits it's maximum height.