(4) Is it possible to define a function which is continuous on a closed, finite interval but does not have an absolute maximum and minimum values? Explain your answer with the help of a graph.

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A: Given:

Q: How can we find the Absolute Extrema of a Continuous Function ƒ on a FiniteClosed Interval?

A: How can we find the Absolute Extrema of a Continuous Function ƒ on a Finite Closed Interval?

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A:

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A: A continuous function in a closed interval is a function whose graphs do not have any breaks in…

Q: true or false?  A continuous function on a closed interval must have a maximum and minimum value.

A: It is true, a continous function on a closed interval must have a maximum and minimum value.

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A: To Determine: What can be said about the extreme values of a function that iscontinuous on a closed…

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A:

Q: Sketch the graph of a function that has an absolute maximum, alocal minimum, but no absolute minimum…

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Q: show that the function has neither an absolute minimumnor an absolute maximum on its natural domain.…

A: Given Data The function is y=1-eˣ/ eˣ+1.   Differentiate the function y=1-eˣ/ eˣ+1 with respect to x…

Q: Sketch the graph of a function ƒ with given properties. (a) ƒ is continuous on [1,5], absolute…

A: Consider the equation

Q: Find the absolute minimum and absolute maximum values of f on the interval below. f(x) = 2x4 - 4x² +…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. 

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Q: Determine whether the following statement is true or false, and explain why. A continuous function…

A: Consider the provided information, A continuous function on an open interval does not have an…

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Q: What is the absolute maximum  what is the absolute minimum

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A: Ques:-   Sketch the graph of a function on the            intervel 3,9 that has as absolute…

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A:

Q: Given the graph below, what can you say about the function at (-1,1)? Not Continuous Continuous

A: The graph of a function is said to be continuous if the value of the function exists for all values…

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A: Sketch the graph of a function that has neither a local maximumnor a local minimum at a point where…

Q: Come up with an example of a continuous on [0, 2] function for which the trapezoidal rule is more…

A: Let us consider a continuous function fx=cosx for x∈0,2. fx is continuous on 0,2 Now, exact value of…

Q: . Does the Extreme Value Theorem guarantee that the following function f must attain an absolute…

A: Solution is here

Q: Is it true that a discontinuous function cannot have both an absolute maximum value and an absolute…

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Q: Explain how a function can have an absolute minimum value at anendpoint of an interval.

A: Consider the function f(x)=x3+2x2+9 defined on interval [-3,2]. We compute maxima and minima of the…

Q: How do you find the absolute maximum and minimum values of a function that is continuous on a closed…

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A: It is known that if f is continuous on a closed interval [a, b], then f has both absolute maximum…

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A:

Q: If f(x) is a continuous, odd function and f(c) is a relative maximum , then f(-c) is a relative…

A:

Q: Sketch the graph of a function on the interval [-3, 4] that has the given properties: • An absolute…

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Q: if f functions is bounded on [a,b] does f has an absolute maximum and absolute minimum or not??

A: if f functions is bounded on [a,b] does f has an absolute maximum and absolute minimum or not??

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A: Definition used -        Absolute value functions-            The absolute value function has a…

Q: Sketch the graph of a function on [-1, 2] that is discontinuous but has both an absolute maximum and…

A: There are many ways to draw the graph with given conditions. One such a graph is as shown below.

Q: What does it mean for a function to be continuous on an interval?Give examples to illustrate the…

A: For open intervalIf f:(a, b)→ℝ is defined on an open interval, then f is continuous on (a, b) if and…

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Q: (3) Construct a function defined on the closed interval [0, 1] with no maximum and minimum. Justify…

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Q: How do you determine the absolute maximum and minimum valuesof a continuous function on a closed…

A: Let f be a continuous function in a closed interval a,b. We will Evaluate f at all the critical…

Q: It is possible for the absolute maximum of a function on a closed interval to occur at:

A: An absolute maximum must occur at a critical point or an endpoint, and x = 0 is the only such…

Q: A function f defined on [a, b] always has an absolute maximum and absolute minimum on [a, b].…

A: False

Q: Sketch the graph of a function on [-1, 2] that has an absolute maximum but no absolute minimum.

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Q: Find the absolute minimum and absolute maximum values of f on the interval below. f(x) = 2x4 - 4x2 +…

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Q: Come up with an example of a continuous on [0, 2] function for which the trapezoidal rule is more…

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Q: If a function is continuous on a closed interval, then the function will have an absolute maximum…

A: