PDM: WS 2.2 (Day 1) Finding Maxima & Minima Values

Directions: In 1 - 4 write the solutions in "interval notation".

1. Using y = -x2 + x + 4 identify the minimum value ______________, maximum value
________________ and range ____________________.
2. What is the maximum value _________________, minimum value ______________ and
3. What is the minimum value __________________, maximum value ________________
and range _____________________ of g(x) = x3 - 4x2 with domain [-1, 4].
4. Find the range to the nearest tenth of f(x) = 2x - x2 with domain [ -1, 4]. _________. 5. Suppose a cylindrical can has a height of 8 inches and a radius of 2.5 inches.
a) Draw a 3 - dim. image & net of this cylinder. 3 - dim.
b) Find the area of the top. ___________What formula did you use? ___________
Show work:

c) Find the area of the middle. _________What formula did you use? __________
Show work:

d) Find the area of the bottom. ________What formula did you use? __________
Show work:

e) What is the surface area of this can? _____________________ f) What is the volume of this can? (Write formula & show work) 2.2 Activity (A): Calculating Maxima and Minima (Day 2)

1. A box needs to be constructed with a square base and hold a volume of 20 cubic meters. Let x be the length
of a side of the base and let h be the height of the box. We need to find the dimensions of the box that will minimize the cost.
a. Write a volume formula for h in terms of x.
b. Find a formula for the surface area of the box as a function of x.
c. Estimate the value of x which minimizes the surface area.
d. Calculate the height and the surface area of the box.
2. Campbell's is designing a new soup can. They need to make a cylindrical can that holds 100 cubic inches.
The manufacturer wants to find the dimensions which require the least amount of metal for each can.
a. Write a volume formula for h in terms of r. b. Find a formula for the surface area of the can as a function of r.
c. Estimate the values of r, h and the surface area.
h: ___________________ SA: _________________
1. Nike needs to make a new shoe box. The box needs to be constructed with a square base and hold a volume
of 1900 cubic inches. Let x be the length of a side of the base and let h be the height of the box. We need to find the dimensions of the box that will minimize the cost.
a. Write a volume formula for h in terms of x.
b. Find a formula for the surface area of the box as a function of x.
c. Estimate the value of x which minimizes the surface area.
d. Calculate the height and the surface area of the box.
2. Old Orchard is designing a new apple juice container. They need to make a cylindrical can that holds 300
cubic inches. The manufacturer wants to find the dimensions which require the least amount of metal for each can.
b. Write a volume formula for h in terms of r. b. Find a formula for the surface area of the cylinder as a function of r.
c. Estimate the values of r, h and the surface area.
h: ___________________ SA: _________________

How Does LYRICA Help? LYRICA works by attaching to a part of the over-firing nerve cells. This is thought to help to reduce the pain signals that cause the symptoms of diabetic nerve pain. It can also be used “off label: that is for similar types of pain problems that the FDA has not examined or approved it for. In any case, this may reduce the nerve pain that can prevent the enjoyment of

Resultate-Übersicht «PferdeWoche» Nr. 44 vom 9. November 2011 Eden, 0/0/35.37; 2. Michel Hendrix (NED), Noble, 0/0/36.95; 3. Ben Schro-eder (NED), Floreen, 0/0/38.00; 10. Andreas Erni (SUI), Chairman, CSI4* Lüttich (BEL) 4.-6. November Grand Prix, A, 1 St.: 1. Patrice Delaveau (FRA), Orient Express, 0/0/38.02; CVI-W München (GER) 5./6. November 2. Eugenie Legrand Angot (FRA), Old