A rectangular building with length L, width W and height H has a surface area given by S=2HW+2LW+2LH The city zoning commission specifies that for all buildings on this particular street the following dimensions must hold L=2W. At the last minute, the building’s owner asks the architects to increase the height of the building; unfortunately the builder have already been given exactly 30,000,000 sqft of siding. Solve the equation for H and create a function H=f(W) which gives the allowable height for a given width. The builder requests a width of 200, use the function H=f(W) to determine the height and length of the building. Under what conditions will H=f(W) be negative? A negative length in this context does not make any physical sense. Create a domain for the function for which (1) all members of the domain are positive (2) all members of the range are positive and not equal to 0 (3) no division by 0.
Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.
A rectangular building with length L, width W and height H has a surface area given by S=2HW+2LW+2LH
The city zoning commission specifies that for all buildings on this particular street the following dimensions must hold L=2W. At the last minute, the building’s owner asks the architects to increase the height of the building; unfortunately the builder have already been given exactly 30,000,000 sqft of siding.
Solve the equation for H and create a function H=f(W) which gives the allowable height for a given width.
The builder requests a width of 200, use the function H=f(W) to determine the height and length of the building.
Under what conditions will H=f(W) be negative?
A negative length in this context does not make any physical sense. Create a domain for the function for which (1) all members of the domain are positive (2) all members of the range are positive and not equal to 0 (3) no division by 0.
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