Intervals of increase and the intervals of decrease?

In summary, the function y=-(x-3)^5(x+1)^4 has a degree of 9 and a negative sign. It is defined in quadrants I, II, and IV. Its roots are x=3 and -1, and the y-intercept is 243. The domain is all real numbers, and the range is also all real numbers. As x approaches negative infinity, y approaches positive infinity, and as x approaches infinity, y approaches negative infinity. The intervals of increase and decrease can be found using derivatives, but since this is not a calculus course and the concept has not been covered yet, it is not possible to determine the specific intervals at this time. However, it can be determined that the
  • #1
BuffaloSoulja
6
0
y=-(x-3)^5(x+1)^4

For this function currently i have:

degree: 9
sign: negative ?
quadrants: I, II and 4
Roots: x=3 and -1
y-intercept= 243
domain: x belongs to E
range: y belongs to E
INTERVALS of INCREASE : ?
INTERVALS of DECREASE : ?
End Behaviors: As x approaches -infinity, y approaches infinity
as x approaches infinity, y approaches -infinity.


For the function y=-(x-3)^5(x+1)^4 what are the intervals of increase and the intervals of decrease?

I have been told to use derivatives. However, this isn't a calculus course and we haven't learned this yet
 
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  • #2
What is true about the derivative when the function is increasing?
 
  • #3
It is positive?
 
  • #4
Yes. Find out when the derivative is positive, and you will have half of your answer.
 

1. What are intervals of increase and decrease?

Intervals of increase and decrease refer to the sections of a graph or function where the values are either increasing or decreasing, respectively.

2. How can I identify the intervals of increase and decrease?

To identify the intervals of increase and decrease, you can look at the slope of the graph or function. If the slope is positive, the interval is one of increase. If the slope is negative, the interval is one of decrease.

3. What do intervals of increase and decrease tell us about a graph or function?

Intervals of increase and decrease can give us information about the overall trend of the graph or function. They can also help us identify critical points, such as maximum or minimum values.

4. Can a graph or function have multiple intervals of increase or decrease?

Yes, a graph or function can have multiple intervals of increase or decrease. This typically occurs when there are multiple critical points or when the function has a complex shape.

5. How can I use intervals of increase and decrease in real-world applications?

Intervals of increase and decrease can be used in various real-world applications, such as analyzing stock market trends, studying population growth, or tracking changes in temperature over time.

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