Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 4x3 – 6x2 – 72x + 7, [-3, 4] absolute minimum value absolute maximum value

Q: let f(x) =4x+3 and g(x) =5x-2. find the function. f-g

A: Topic:- function

Q: Find the domain of each function

A: we have to find the domain of the given function. G(x)=x+4x3-4x

Q: Let f(x) = Calculator x2-3x - 18 x-2 Check Answer Write the domain of f as an interval.

A: We need to find out the domain of the given function.

Q: State the relative minimums and relative maximums for the function f(x) = x³ - 6x² - 288x + 144

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Q: Find the local maximum and the local minimum values of f. 7 want to use either the sign chart or the…

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Q: When f(x) = 7x² + 6x + 2, evaluate f(- 1) f(-1) = Question Help: Video Submit Question

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Q: Graph the function f(x)=√√x + 9. 3 What are the minimum and maximum values on the interval [-10,…

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Q: Find the point on the graph of the function f that is closest to the point (a, b) by minimizing the…

A: According to the given information, it is required to find a point on the graph that is closest to…

Q: Find the domain and range of the function f. Consider the function f defined by f(r² + 1) = x* + 5æ²…

A: The domain of a function is the set of values for which the function is defined. The range of 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.