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: _________________

Por/ Ernesto Rios Juan Bautista Alberdi –el gran ausente del Congreso Constituyente de 1853[1]- fue el corifeo argentino del liberalismo en boga en ese entonces, que imprimió a la Constitución[2] su sesgo individualista, su fundamentación iluminista[3], y su estructuración como pieza central para “poner en manos ajenas el usufructo de nuestras riquezas y hasta el control intern