Showing increasing or decreasing

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Homework Help Overview

The discussion revolves around determining whether the function f(x) = 2x^3 + 3x^2 - 36x + 5 is increasing or decreasing on the interval [-1, 1].

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the use of the derivative to analyze the behavior of the function, questioning where f' is greater than or less than zero. There is also consideration of evaluating the function at the endpoints of the interval and checking for critical points within the specified domain.

Discussion Status

Some participants have provided insights into evaluating the function at the endpoints and checking for critical points, suggesting that the function appears to be decreasing based on these evaluations. However, there is still an emphasis on confirming the behavior of the function within the given interval.

Contextual Notes

Participants note the importance of the specified domain [-1, 1] and the implications of critical points that lie outside this interval.

kathrynag
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Homework Statement


Is f increasing or decreasing on f(x)=2x^3+3x^2-36x+5 on [-1,1]



Homework Equations





The Attempt at a Solution


f'(x)<0 for all x in (a,b), then x,y and x, y in [a,b] implies f(x)>f(y) and f is decreasing
 
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So put that idea together with the function you are given. Where is f' > 0? Where is f' < 0? Be sure to consider the domain you're given.
 
Ok that makes sense
 
If you are allowed to use derivatives then I would evaluate f(-1) = 42 and f(1) = -26 so it would appear that it's decreasing but we need to check if there are any critical points in [-1, 1]. So let's evaluate the derivative and we get [tex]f'(x) = 6x^{2} + 6x - 36[/tex] so if we set it equal to 0 we get x = -3, 2 both of which are not in our domain so I would think we are done.
 

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