Showing increasing or decreasing

In summary, f is decreasing on the interval [-1,1] for the given function f(x)=2x^3+3x^2-36x+5, as f'(x)<0 for all x in (-1,1) and there are no critical points in the domain.
  • #1
kathrynag
598
0

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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  • #2
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.
 
  • #3
Ok that makes sense
 
  • #4
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.
 

Related to Showing increasing or decreasing

What is the meaning of "showing increasing or decreasing" in scientific research?

"Showing increasing or decreasing" refers to the trend or pattern of change observed in data over time or across different conditions. It is often used to describe the relationship between two variables, where one variable is consistently increasing or decreasing in response to changes in the other variable.

How is "showing increasing or decreasing" different from "showing a positive or negative correlation"?

The terms "showing increasing or decreasing" and "showing a positive or negative correlation" are often used interchangeably, but they have different meanings. "Showing increasing or decreasing" refers to the overall trend of change in data, while "showing a positive or negative correlation" specifically describes the direction and strength of the relationship between two variables.

What are some common methods for visually showing increasing or decreasing data?

Some commonly used methods for visually showing increasing or decreasing data include line graphs, bar graphs, and scatter plots. These graphs allow for a quick and easy comparison of data over time or across different conditions.

What factors can affect the accuracy of "showing increasing or decreasing" data?

There are several factors that can affect the accuracy of "showing increasing or decreasing" data, such as sample size, data collection methods, and external variables. It is important for scientists to carefully consider these factors when interpreting and presenting their data.

Why is it important to show whether data is increasing or decreasing in scientific research?

Showing whether data is increasing or decreasing is important in scientific research because it can provide valuable insights into the relationship between variables and can help identify patterns or trends. This information can then be used to make informed conclusions and inform future research studies.

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