Locate the absolute extrema of the function y=x^2-2-cosx

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In summary, the user is having difficulty with completing a final exam from their engineering calc class. Seven questions are provided, and if anyone has any helpful advice on how to complete them, it would be greatly appreciated.
  • #1
dontgetit
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Im Stuck!

I have a final exam coming up in my engineering calc class. I am at a loss for how to complete some of the 238570198437049870958273049875 problems he gave us for a review. I thought I did well on the exam covering the material but i got a 63. Apparently I am not understanding SOMETHING. These are the seven questions i missed on the exam...if ANYONE wants to give their imput on how to complete them in order for me to compare what i did, to the correct way to do it...id appreciate it.

1. locate the absolute extrema of the function y=x^2-2-cosx on the closed interval [1,3].

2. Using Rolle's Theorem, find all values of c for the function f(x)=cosx in the open interval [0,2pi] such that f ' (c)=0

3. Using the Mean Value Theorem find the values for c of the function f(x)=arctan(1-x), [0,1]

4. Find the critical numbers of f. find the open intervals on which the function is increasing or decreasing and locate all relative extrema. f(x)=[(x^3)/3]-lnx

5. consider the function on the interval (0,2pi). for the function f(x)=(sinx)/(1+cos^2x) a)find the open intervals on which the function is increasing or decreasing, b)apply the first derivative test to identify all relative extrema

6. find the points of inflection and discuss the concavity of the graph of the function f(x)=x^3(x-2)

7. find all relative extrema. use the second derivative test where applicable. f(x)=arcsin x - 2x
 
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  • #2
Nice user-name. Welcome to PF.

Typically, it's a no-no to just answer questions without the person showing work. Plus, it's easier for us, and more helpful to you, if you post how you attempted to solve these problems and we discuss where you went wrong on your particular solutions.

But just looking at the problems you posted, you seem to be having a lot of trouble with finding extrema and how derivatives relate to extremal points.

In general, use as many resources as possible when reviewing things. I often use Wikipedia, for example, when I need help understanding a concept, because its explanation might be different than my textbook's, and that may provide some insight. Sometimes it just takes the right wording to make a concept "click". Mathworld is another good site to use, although sometimes the explanations are a bit advanced.
 
  • #3
Ok, so where is your work?
 
  • #4
Every one of these simply requires that you find the derivatives of certain functions and then do things with them. You can meet our "show some work" criterion by telling us what the derivative of the function in each problem is and then we'll help you "do thing with them".
 
  • #5
Yea understandable, Ill put my work up right now. Like I said, these are problems that I missed from our last exam, so they are all pretty much the same, and I am not sure what it is that I am missing, but maybe by putting up what I tried solving on the exam will help you guys help me figure out where I am going wrong.


Give me a few minutes to type it all out and ill put them up. Thanks for your help.
 

FAQ: Locate the absolute extrema of the function y=x^2-2-cosx

What is the purpose of finding the absolute extrema of a function?

The absolute extrema of a function helps us identify the highest and lowest points of the function, which can provide valuable information about the behavior and characteristics of the function. It can also help in solving optimization problems.

How do you find the absolute extrema of a function?

To find the absolute extrema of a function, we need to first take the derivative of the function and set it equal to zero. Then, we solve for the critical points of the function. Next, we evaluate the function at each critical point and the endpoints of the given interval. The highest and lowest values will be the absolute extrema of the function.

What is the difference between absolute extrema and relative extrema?

Absolute extrema are the highest and lowest values of a function over a given interval. They are also known as global extrema. On the other hand, relative extrema are the highest and lowest values of a function within a specific range or subset of the given interval. They are also known as local extrema.

How do you handle finding the absolute extrema of trigonometric functions?

For trigonometric functions, we follow the same steps as finding the absolute extrema of any other function. We first take the derivative of the function and set it equal to zero. Then, we solve for the critical points and evaluate the function at those points as well as the endpoints of the interval. However, we may need to use trigonometric identities and solve for the critical points using inverse trigonometric functions.

Can a function have more than one absolute extrema?

Yes, a function can have more than one absolute extrema. For example, a cubic function can have two absolute extrema, one being the global maximum and the other being the global minimum. This can occur when the function has multiple critical points within the given interval.

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