 ### Find a polynomial of the specified degree that has the given zero. Degree 4 with zeros -4, 3, 0, and -2.

This question aims to find the polynomial with a degree 4 and given zeros of -4, 3, 0, and -2. The question depends on the concepts of polynomial expressions and the degree of polynomials with zeros. The degree of any polynomial is the highest exponent of its independent variable. The zeros of a polynomial are […]

### (a) Find the average value f on the given interval. (b) Find c such that f_{ave} = f(c). Equation given below

This problem aims to find the average value of a function on a given interval and also find the slope of that function. This problem requires knowledge of the fundamental theorem of calculus and basic integration techniques. To find the average value of a function on a given interval, we will integrate and divide the […]

### 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 […]

### Use a linear approximation (or differentials) to estimate the given number. (1.999)^5

The aim of this article is to find the value of a given number raised to a degree. The basic concept behind this article is the use of Linear Approximation or Differential to calculate the value of a given function or a number. Linear Approximation or Linearization is a method used to approximate or estimate […]

### 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 […]