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: _________________
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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