A rectangular package to be sent by a postal service that has a maximum total length and perimeter (or girth) limit of 108 inches. A rectangular package is to be sent via this service. Calculate the dimensions of the package that covers the maximum volume. (Cross-sections may be assumed to be square)

This question aims to learn the basic methodology for optimizing a mathematical function (maximizing or minimizing). Critical points are the points where the value of a function is either maximum or minimum. To calculate the critical point(s), we equate the first derivative’s value to 0 and solve for the independent variable. We can use the […]

Find two functions f and g such that (f ∘ g)(x) = h(x).

[ h(x) = (x + 2)^3 ] The question aims to find the functions f and g from a third function which is a composition of the function of those two functions. The composition of functions can be defined as putting one function into another function that outputs the third function. The output from one […]