Global Extrema of a Function: Finding the Maximum and Minimum Values

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Homework Help Overview

The discussion revolves around finding the maximum and minimum values of a function, specifically focusing on the concept of global extrema. The original poster indicates challenges due to the absence of real roots for the derivative of the function.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants explore the implications of having no real values for which the derivative equals zero, questioning the existence of local maxima or minima and considering the possibility of other types of extrema.

Discussion Status

The discussion is ongoing, with participants raising questions about the nature of extrema in the absence of real roots. Some guidance has been offered regarding reviewing textbook material on global extrema, but no consensus has been reached on the implications of the findings.

Contextual Notes

There is a mention of the need for a graph, potentially involving imaginary numbers, and a suggestion that the exercise may seem meaningless due to the lack of real extrema.

oswald88
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Homework Statement



Find max and min value of the function

Homework Equations



attached.

The Attempt at a Solution



no graph, because roots aren't real numbers.
 

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As you've found, there are no real values of [itex]x[/itex] where [itex]f'(x)=0[/itex]...what does that tell you about the existence of local maxima/minima? Are there other types of extrema? Where might they occur?
 
no idea! need imaginary graph? maybe there isn't any max or min.. so the exercices question is meanless.
 
You need to read the section n your textbook on global extrema.
 

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