Microsoft word - 2.2 max & min activity (day 1 )

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: _________________

Source: http://blogs.reeths-puffer.org/prattl/files/2012/10/PDM_2.2WS.pdf

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