A box with a square base and open top must have a volume of 78732 cm, We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only æ, the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of r.] Simplify your formula as much as possible. A(z) = Next, find the derivative, A'(x). A' (x) = %3! Now, calculate when the derivative equals zero, that is, when A (z) 0. [Hint: multiply both sides by .) %3D A'(x) = 0 when = %3D We next have to make sure that this value of x gives a minimum value for the surface area. Let's use the second derivative test. Find A"(x). A"(x) = %3D Evaluate A"(x) at the r-value you gave above. NOTE: Since your last answer is positive, this means that the graph of A(x) is concave up around that value, so the zero of A'(x) must indicate a local minimum for A(). (Your boss is happy now.)
A box with a square base and open top must have a volume of 78732 cm, We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only æ, the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of r.] Simplify your formula as much as possible. A(z) = Next, find the derivative, A'(x). A' (x) = %3! Now, calculate when the derivative equals zero, that is, when A (z) 0. [Hint: multiply both sides by .) %3D A'(x) = 0 when = %3D We next have to make sure that this value of x gives a minimum value for the surface area. Let's use the second derivative test. Find A"(x). A"(x) = %3D Evaluate A"(x) at the r-value you gave above. NOTE: Since your last answer is positive, this means that the graph of A(x) is concave up around that value, so the zero of A'(x) must indicate a local minimum for A(). (Your boss is happy now.)
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter59: Areas Of Rectangles, Parallelograms, And Trapezoids
Section: Chapter Questions
Problem 79A
Related questions
Question
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 7 steps with 1 images
Recommended textbooks for you
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL