# the greatest negative solution

• Jan 8th 2011, 10:08 AM
kennie0325
the greatest negative solution
This is an exercise from a subject called Math Laboratory in my university and the aim is to solve this using software Maxima.

Consider the following function:

F(x)=2sin(4(x-[1/2]))+sin(x-[1/2])

a) find the greatest negative solution
b) the fourth positive solution

Regards,
• Jan 8th 2011, 10:14 AM
snowtea
Quote:

Originally Posted by kennie0325
the aim is to solve this using software Maxima.

I don't understand. If the software already tells you where the Maxima occur, then you can just read the results to answer your question.
• Jan 8th 2011, 12:18 PM
CaptainBlack
Quote:

Originally Posted by kennie0325
This is an exercise from a subject called Math Laboratory in my university and the aim is to solve this using software Maxima.

Consider the following function:

F(x)=2sin(4(x-[1/2]))+sin(x-[1/2])

a) find the greatest negative solution
b) the fourth positive solution

Regards,

In closed form or numerically?

CB
• Jan 8th 2011, 12:46 PM
kennie0325
numerically. I suppose this has to be solved by creating a routine based on Newton's method or Rolle's theorem...(Thinking)

Thank you.

Ken
• Jan 8th 2011, 12:49 PM
kennie0325
I just would like know the steps I should make in Maxima in order to find the solutions.

Thanks

Ken
• Jan 8th 2011, 07:48 PM
CaptainBlack
Quote:

Originally Posted by kennie0325
I just would like know the steps I should make in Maxima in order to find the solutions.

Thanks

Ken

Plot the function over the interval [-5,5] and identify intervals containing the required root and no other from the plot. Then use the find_root function to refine the solution.

Or use the plot to identify the approximate positions of the required roots and newton to refine the solution.

CB
• Jan 9th 2011, 01:53 PM
kennie0325
actually i'm not understanding the question "the greatest negative solution"..
does this mean the same as the absolute minimum?
I've plot the function then identified an interval where the minimum is.
Then i've differentiated the function to check where y=0.
I've got the approximated x value of the absolute minimum, using rolle.

But I guess this is not the greatest negative value (Wondering)

Many thanks!

Regards,

Ken
• Jan 9th 2011, 01:55 PM
kennie0325
by the way, what should I undestand as the fourth positive solution?

Thank you again!

Ken
• Jan 9th 2011, 01:56 PM
CaptainBlack
Quote:

Originally Posted by kennie0325
actually i'm not understanding the question "the greatest negative solution"..
does this mean the same as the absolute minimum?
I've plot the function then identified an interval where the minimum is.
Then i've differentiated the function to check where y=0.
I've got the approximated x value of the absolute minimum, using rolle.

But I guess this is not the greatest negative value (Wondering)

Many thanks!

Regards,

Ken

The greatest negative solution is the negative solution closest to zero

CB