Finding minimum and maximum of function

[Habe]

I need a help!
The following function has two minimum and one local maximum, but I do not know how to find the coordinates of these points. y= -9.18894-3x²/50+9.18894cosh(0.108826x)
Could anybody help to solve this problem?!

 

[Deleted member 4993]

I need a help!
The following function has two minimum and one local maximum, but I do not know how to find the coordinates of these points. y= -9.18894-3x²/50+9.18894cosh(0.108826x)
Could anybody help to solve this problem?!

Is your problem:

y = -9.18894 - (3x²/50) + 9.18894 * cosh(0.108826*x) ............. this is what you have posted.

How do you find local minimum/maximum of any function? (think about derivatives).

What does your textbook/class-notes say?


You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...217#post322217

We can help - we only help after you have shown your work - or ask a specific question (not a statement like "Don't know any of these")

Please share your work with us indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[Habe]

Of course Khan there is no any problem with finding derivatives at all. It is so easy to discuss that.
So the first derivative is the following:
y'= -6x/50+9.18894*0.108826*sinh(0.108826x)
The y'=0 is a transcendental equation, which I would like to solve. So I ask you do you know to solve that? Hope it is now clear it is not a question about using derivatives for finding minimum/maximum of any function.

Is your problem:

y = -9.18894 - (3x²/50) + 9.18894 * cosh(0.108826*x) ............. this is what you have posted.

How do you find local minimum/maximum of any function? (think about derivatives).

What does your textbook/class-notes say?


You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...217#post322217

We can help - we only help after you have shown your work - or ask a specific question (not a statement like "Don't know any of these")

Please share your work with us indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[Habe]

Of course Khan there is no any problem with finding derivatives at all. The first derivative is the following:

y'= -6x/50+9.18894*0.108826*sinh(0.108826x)

y'=0 is a transcendental equation what I would like to solve. So I ask you: do you know how to solve it? Hope it is now clear that it is not a question about using derivatives for finding minimum/maximum of any function.

 

[HallsofIvy]

In general, you can't solve such an equations in terms of "elementary functions". The cosh can be written in terms of exponentials so you probably could convert to something involving "\(\displaystyle xe^x\)" and so solved in terms of the "Lambert W" function which is defined as the inverse function to \(\displaystyle f(x)= xe^x\). You could also use some kind of numerical solution to get an approximate solution.

 

[DrPhil]

Of course Khan there is no any problem with finding derivatives at all. The first derivative is the following:

y'= -6x/50+9.18894*0.108826*sinh(0.108826x)

y'=0 is a transcendental equation what I would like to solve. So I ask you: do you know how to solve it? Hope it is now clear that it is not a question about using derivatives for finding minimum/maximum of any function.

The equation y'=0 can be written

sinh(0.108826 x) = 0.12 x

In this form the first solution for x should be apparent.
I would use successive approximations to find the other pair - after noting that the equation is symmetric about x=0, so if you find a positive root then the negative of that root is also a root.

 

[JeffM]

Of course Khan there is no any problem with finding derivatives at all. The first derivative is the following:

y'= -6x/50+9.18894*0.108826*sinh(0.108826x)

y'=0 is a transcendental equation what I would like to solve. So I ask you: do you know how to solve it? Hope it is now clear that it is not a question about using derivatives for finding minimum/maximum of any function.

Based on your original question, how would anyone have known that you were asking for help in finding a numerical approximation?

If you ask a vague question, you may not get a pertinent answer to the specific question that you failed to ask.

I have a question for you. Did you read Read before Posting before you posted?

 

[Habe]

Thank you Dr Phil for help. According to your constructive instructions the solution is:

x1=0 (local maximum),
x2=7.1 (minimum),
x3= -7.1 (minimum).