1. Bellwork:

2. PRE CALCULUS
Section 4.7
Forming Functions from Verbal Descriptions

3. Manufacturing and Volume/Rate Problems

4. Objective
To form a function of one variable from a verbal description and, when appropriate, to determine the minimum or maximum value of the function.

5. A box with a square base and top has a
volume of 10 meters cubed. The material
for the base costs $12 per square meter
and the material for the sides costs $8 per
square meter. Express the cost C of the
material as a function of the width.

6. Water flows into a conical tank 100 cm
wide and 250 cm deep at a rate of
40 cubic centimeters per second. Find
the volume in terms of the height of the
tank and the height in terms of the time.

7. Water is flowing into a cylindrical tank
at 6 cubic meters per second. The radius
is 20 meters and the height of the tank is
100 meters. Find the volume in terms of
the height of the tank and the height in
terms of the time.

8. P(x,y) is an arbitrary point on the parabola y = x2
P(x,y) is an arbitrary point on the parabola y = x2. Express the distance, d, from P to the point A (2,1) as a function of the x-coordinate of P.

9. Ticket to leave:
A cylinder with no top has a volume of 20 m3. Express the total surface area of the box as a function of the radius, r, of the base.

10. Bellwork
Lesson 4.7
P Written Ex (1, 5, 7-12all)