You are given the graph of a function f defined on the indicated interval. Find the coordinates of the absolute maximum and the absolute minimum of f, If they exist. (If an answer does not exist, enter DNE.) 1. f defined on -1, 3] maximum (x, y) = minimum (x, y) =

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A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

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A: The given function is fx=axebx. It is given that f15=1. So, f15=a·15·eb·151=aeb55aeb5=5

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A: Option (C) is correct. Because the given function is continuous in the interval [0 4].

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Q: Please show your answer to at least 4 decimal places. Suppose that f(x, y) = x2 – xy + y? – 3x + 3y…

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Q: Find the absolute maximum and minimum of f(x, y) = 3x + 5y within the domain x² + y? < 25. 1.…

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Q: On the graph of f(x) = cos x and the interval [-27, 0), for what value of x does f(x) achieve a…

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Q: (b) Sketch the graph of a function that has a local maximum at 3 and is continuous but not…

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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.