AP Calculus AB
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07/20/22 Perkins AP Calculus AB Day 12 Section 3.7
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AP Calculus AB. Day 12 Section 3.7. 1.An open box having a square base and a surface area of 108 square inches is to have a maximum volume. Find its dimensions. Primary. Secondary. Domain of x will range from x being as small as possible to x as large as possible. Largest - PowerPoint PPT Presentation
Transcript of AP Calculus AB
04/19/23 Perkins
AP Calculus AB
Day 12Section 3.7
1. An open box having a square base and a surface area of 108 square inches is to have a maximum volume. Find its dimensions.
Primary Secondary2V x y
Intervals: 0,6 6, 108Test values: 1 10
V ’(test pt) V(x) inc dec
rel max
6x
xx
y2108 4x xy
2108
4
xy
x
22 108
( )4
xV x x
x
3108
4 4
x x
31427x x
234'( ) 27V x x
23427 0x
2 4327x
6x
Domain of x will range from x being as small as possible to x as large as possible.Smallest
(x is near zero)
Largest
(y is near zero)2 108x 0x
2 4SA x xy
21 8 6
6
0
4y
3 y
Dimensions: 6 in x 6 in x 3 in
2. A rectangular page is to contain 24 square inches of print. The margins at the top and bottom are 1.5 inches. The margins on each side are 1 inch. What should the dimensions of the print be to use the least paper?
Primary Secondary
2 3A x y 24xy
11
1.5
1.5
224 in
x
2x
y3y 24
xy 24( ) 2 3xA x x 4824 3 6xx 13 48 30x x
248'( ) 3x
A x 2
2
3 48x
x
crit #'s: 0, 4x Intervals: 0,4 4,24Test values: 1 10
A ’(test pt) A(x) incdec
rel min
4x
Smallest
(x is near zero)
Largest
(y is near zero)
24x 0x
44
2y
6y
Print dimensions: 6 in x 4 in
Page dimensions: 9 in x 6 in
Perkins
AP Calculus AB
Day 12Section 3.7
1. An open box having a square base and a surface area of 108 square inches is to have a maximum volume. Find its dimensions.
2. A rectangular page is to contain 24 square inches of print. The margins at the top and bottom are 1.5 inches. The margins on each side are 1 inch. What should the dimensions of the print be to use the least paper?
