An open box of maximum volume is to be made from a square piece of material, s = 12 inches on a side, by cutting equal squares from the coners and turning up the sides (see figure). S-2r X (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) Height, xLength and Width Volume, V 12 2(1) 1 1[12 2(1)12 2[12 2(2)12 = 100 12 2(2) 2. = 128 3[12 2(3)12 12 2(3) 3 12 2(4) 4[12 2(4)]2 4 12 2(5) 5[12 2(5)]2 12 2(6) 6[12 2(6)]2 Use the table to quess the maximum volume. =A (b) Write the volume Vas a function of x. 0 x

Question

How can I get the result?

Which is the result?

An open box of maximum volume is to be made from a square piece of material, s = 12 inches on a side, by cutting equal squares from the
coners and turning up the sides (see figure).
S-2r
X
(a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.)
Height, xLength and
Width
Volume, V
12 2(1)
1
1[12 2(1)12
2[12 2(2)12
= 100
12 2(2)
2.
= 128
3[12 2(3)12
12 2(3)
3
12 2(4) 4[12 2(4)]2
4
12 2(5) 5[12 2(5)]2
12 2(6) 6[12 2(6)]2
Use the table to quess the maximum volume.
=A
(b) Write the volume Vas a function of x.
0 x<6
(c) Use calculus to find the critical number of the function in part (b) and find the maximum value.
V =
(d) Use a
graphing utility to graph the function in part (b) and verify the maximum volume from the graph.
V
V
120
15
100
80
10
60
40
20
X
2
4
5
6
X
0.5
1.0
1.5
2.0
2.5
3.0
V
V
60
120
50
100
40
80
30
60
20
40
10
20
X
6
1
X
2
3
4
5
3
5
2
S 2r

Image Transcription

An open box of maximum volume is to be made from a square piece of material, s = 12 inches on a side, by cutting equal squares from the coners and turning up the sides (see figure). S-2r X (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) Height, xLength and Width Volume, V 12 2(1) 1 1[12 2(1)12 2[12 2(2)12 = 100 12 2(2) 2. = 128 3[12 2(3)12 12 2(3) 3 12 2(4) 4[12 2(4)]2 4 12 2(5) 5[12 2(5)]2 12 2(6) 6[12 2(6)]2 Use the table to quess the maximum volume. =A (b) Write the volume Vas a function of x. 0 x<6 (c) Use calculus to find the critical number of the function in part (b) and find the maximum value. V = (d) Use a graphing utility to graph the function in part (b) and verify the maximum volume from the graph. V V 120 15 100 80 10 60 40 20 X 2 4 5 6 X 0.5 1.0 1.5 2.0 2.5 3.0 V V 60 120 50 100 40 80 30 60 20 40 10 20 X 6 1 X 2 3 4 5 3 5 2 S 2r

Expert Answer

Want to see the step-by-step answer?

See Answer

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

See Answer
*Response times vary by subject and question complexity. Median response time is 34 minutes and may be longer for new subjects.
Tagged in

Related Calculus Q&A

Find answers to questions asked by student like you

Q: I need help with this please. How do I find the volume generated by revolving the region bounded by ...

A: Given information:The region bounded by y = -sinx and y=0, from x= -2pi to x=0, about the x-axis

Q: Evaluate the integral. Please refer to image.

A: Obtain curl F as follows.

Q: Only problem I'm stuck on for this assignment please help!

A: Hi there! The question is having many sub-parts. Since no specification is given, only first three s...

Q: y′=−2ex −9x2 +x+4 y(0)=6 Solve the initial value problem above. Do not include "y=" in your answer.

A: Solve the Initial Value Problem(IVP) for first degree differential equation is given.

Q: 3 dx = 1 2x 8 In 국 5 -4 In 2 In을 -2 In -8 In LOn LOn

A: Obtain the value of the integral as follows.The given integral is,

Q: I need step by step with explanations, because I turned my brain off and I’m having trouble turning ...

A: (a)The function is f(x) = sin4(4x5).

Q: Evaluate the integral in cylindrical coordinates. Please see attached image.

A: To calculate the value of the integral in cylindrical coordinates which is shown below,

Q: Consider the function g(x) = |(x^2 - 4)/(x+3)| do the following: a) Give the domain of the function ...

A: a) First obtain the singularity for the given function as follows.The denominator of the given fract...

Q: Determine if y=ex −7x−4 is a solution to y′−y=7x−3.

A: To test whether the given function y(x) is a solution of the given differential equation