Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x4 − 50x2 + 3 (a) Find the interval on which f is increasing. (Enter your answer using interval notation.)       Find the interval on which f is decreasing. (Enter your answer using interval notation.)       (b) Find the local minimum and maximum values of f. local minimum value           local maximum value           (c) Find the inflection points. (x, y) =                 (smaller x-value) (x, y) =                 (larger x-value)Find the interval on which f is concave up. (Enter your answer using interval notation.)       Find the interval on which f is concave down.(Enter your answer using interval notation.)

Q: Find the domain of the function. (Enter your answer using interval notation.) g(x) = V² - 6x

A:

Q: Find the maximum or minimum value of the function. y = x2 − 8x + 19

A: To find the maximum or minimum value of the function. y = x2 − 8x + 19.

Q: Find the domain of the function. (Enter your answer using interval notatio f(x) = Vx + V2 - x

A: We will find the domain of function

Q: 3. Let f(x) = 3x² + 1 and g(x) = x + 4. Find (f+g)(x) and (f- g)(x) and state the domain of each.

A: Given,

Q: Determine the location of each local extremum of the function. f(x) = x3+7/2 x2 + 12x + 4

A:

Q: 3. Let f(x) = 3x² + 1 and g(x) = x + 4. Find (f+g) (x) and (f- g)(x) and state the domain of each.

A:

Q: Find the domain of the function. (Enter your answer using interval notation.) х f(x) 3x – 5 Зх —

A:

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.