Find Maximum Value of f(x)+x | Derivative Question

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Homework Help Overview

The discussion revolves around finding the maximum value of the function f(x) + x, where f(x) is defined as a quadratic function, specifically f(x) = -x² + 4x - 5. Participants are exploring methods to determine this maximum value.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the use of derivatives to find critical points, as well as the method of completing the square to analyze the function's vertex. There is also mention of a discrepancy between calculated answers and a teacher's provided answer.

Discussion Status

The conversation includes various approaches to the problem, with some participants suggesting derivative methods while others mention completing the square. There is acknowledgment of differing answers, but no consensus has been reached regarding the correct maximum value.

Contextual Notes

Participants note that there may be confusion regarding the correct maximum value, as one participant references a test answer that differs from their calculations. The original poster expresses concern about their understanding of the problem.

Clu2.0
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1. f(x)=-x2+4x-5 (parabola)

What's the maximum value of "f(x)+x"?


sorry for my english :)
 
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Clu2.0 said:
1. f(x)=-x2+4x-5 (parabola)

What's the maximum value of "f(x)+x"?


sorry for my english :)
Since f(x)= -x2+ 4x- 5, f(x)+ x= -x2+ 5x- 5. That can be written as -(x2- 5x- 5. Now complete the square to dotermine where the vertex is.
 
thanks ok find the answer ("1") but in the test answer is 5/4 and teachers says it's correct
 
Isn't this just a simple case of taking the first derivative with respect to x and setting it equal to zero? This then tells you the value of x where the maximum value occurs. Then substituting this value into the function f(x)+x will tell you the maximum value at that point. This procedure does give the correct answer of 5/4.
 
thanks a lot, my carelessness
 
Or via completing the square.
 

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