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## 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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