+ Give the global maximum and global minimum values for the given functions on the given regions, or state that it does not exist.

Q: •Create a piecewise function with four constraints. •Use transformations of four different parent…

A: A function is said to be piecewise function if we substitute different value of x lying in distinct…

Q: Where does a local minimum occur?

A: given,      Local minimum .

Q: Indicate the values of the global maximum and global minimum for the function, f(x) = xlnx, as well…

A: f(x)=xln(x)f'(x)=ln(x)+x.1xf'(x)=1+ln(x)now f'(x)=01+ln(x)=0ln(x)=-1x=e-1x=0.3678

Q: f (x)= xª + 4x³ – 4x 3 1

A:

Q: what about the local minimum?

A: To find the point(s) of local minimum in the following graph.

Q: Explain the difference between an absolute minimum and alocal minimum.

A:

Q: Let f (x) = (x – 4)²/3_ Find the intervals on which f is increasing and decreasing.

A:

Q: 4. y= 3x^4 + 3y - x^2 +7 * O Implicit Function O Explicit Function 5. y= x^4 + 2x^2 - 4 * O Implicit…

A:

Q: A rectangular pen is built with one side against a barn. Find the dimensions of the pen that will…

A: A rectangular pen is built with one side against a barn. Findthe dimensions of the pen that will…

Q: . Consider the following function.  f(x)=x^5ln(x) 3a)Use calculus to find the minimum value.

A:

Q: Determine whether the statement "Between any two relative minima of f, there must be at least one…

A: Determine whether the statement "Between any two relative minima of f, there must be at least one…

Q: If 2x +y= 10, find the minimum value of x+ y2

A:

Q: Every function defined on a closed interval [a, b] must have a global maximum and a global minimum…

A: Find your answer below

Q: Is there an informal way to think about relative maximum and relative minimum?

A:

Q: Give an example that: the absolute maximum is not a local minimum.

A: Consider an example of the function:  in a interval [-2,3]

Q: The cost of producing x units of a product during amonth is x2 dollars. Find the minimum cost method…

A: Introduction: Lagrange multipliers is a technique used in calculus to find the extrema of a…

Q: or values of x which the given the function y=x+1, has a 4.) Find the value maximum or a minimum…

A: You need to find out the critical points then solve for maxima & minima. The explanation part is…

Q: Find the minimum value ofx +y +z² given x+y+z=3a.

A:

Q: what is the minimum value of y=–8+2cos4x?

A: Given, y = –8 + 2cos4x  We have to find the minimum value of  y = –8 + 2cos4x   When we have the…

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.