Sketch the graph of a function ƒ with given properties. (a) ƒ is continuous on [1,5], absolute maximum at 5, absolute minimum at 2, local maximum at 3, local minima at 2 and 4 and 1 is neither an absolute maximum nor a minimum.

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A: Consider the statement: A set of points in the xy-plane is the graph of a function if and only if…

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A: Solve by finding minima and maxima

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A:

Q: Sketch the graph of a function f on [0, 4] with a discontinuity such that f has an absolute minimum…

A: To Sketch the graph of a function f on [0, 4] with a discontinuity such that f has an absolute…

Q: 1. How to determine whether the function is continuous or not at a certain point?

A: As per our guideline we are supposed to be answer only one question please repost the other question…

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A:

Q: 2) Sketch the graph of a function f that is continuous on [1,5] such that f has absolute minimum at…

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A: Consider the function Then and The graph of the function is shown below,

Q: Sketch the graph of a function f that is continuous on [1, 5] and has the given properties.…

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A:

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A:

Q: If a function is not continuous at a point, then it is not defined at that point

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A: Part (b)

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Q: (a) find the function’s domain, (b) find the function’srange, (c) describe the function’s level…

A: Hey, since there are multiple sub-parts posted, we will answer first three sub-parts. If you want…

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A: Find your answer below

Q: Sketch the graph of a function f with domain [1, 5] satisfying all the following conditions: •…

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Q: Let f(x) = x³ –x² – 12x+2. Find the global maximum and minimum of f(x) over the interval [-2,1].…

A: THE EXPLANATION HAS BEEN GIVEN IN THE ATTACHED FILE.

Q: Sketch a graph of the function f(x) = 2 sin(z) %3D 6+ 5 4 3 -6 -5 -4 -3 -2 -1 -- 6 7 -9 -8 -7 2 3 5…

A: How to solve: make a graph of sin(x) and then transform it one by one:

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Q: 1. Sketch the graph of a continuous function f on [-2, 5] satisfying the following properties: f'(x)…

A: Explanation of the answer is as follows

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Q: Sketch the graph of a function f with domain [1,5] satisfying all the following conditions: •…

A: This question can be solved using the concept of nature of graphs.

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Q: Find the global maximum and minimum of the function f(x)=√3−2x on the interval [−3,1).

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A: It is supposed that f is a function with

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.