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.
Use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function : f(x) = -11x4 - 6x2 + x + 3
Consider the provided function,
Use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function.
The graph of the polynomial function eventually rises or falls depends on the leading coefficient and the degree of polynomial function.
So, there are 4 cases,
When n is odd and the leading Coefficient is positive then the graph falls to the left and rises to the right.
When n is odd and leading Coefficient is negative then the graph rises to the left and falls to the right.
When n is even and leading Coefficient is positive then the graph rises to the left and right.
When n is even and leading Coefficient is negative then the graph falls to the left and right.
Here we can see that the leading Coefficient is .
And the degree is even.
So, the our graph falls to the left and right.
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