# Math Help - Monotine decreasing functions...

1. ## Monotine decreasing functions...

Hey all,

Its me again, sorry long time since I have been here, im back with another problem, hopefully you guys can help me.

I have been asked to write a matlab file to show that: f (x) = cos(x²) is monotone decreasing on the interval [o,root(pi/2)]

I know before I start, that I need to used an argument, il call it n, and after the argument has been done, return the upper and lower Riemann sums for f over this interval whilst still having n in equal strips, so I have begun with:

Originally Posted by MATLAB SHIZ
function [ U,L ] = sums( n )
% finds upper and lower sums for
% cos(x^2) from 0 to sqrt(pi/2)
% with n equal intervals
% xi contains the points in the dissection
% U is the upper sum
% L is the lower sum
Now I need to set the paramaters, but im quite stuck with it, wonder if any of you can help me?

Regards,
Jason

2. Originally Posted by ramdrop
Hey all,

Its me again, sorry long time since I have been here, im back with another problem, hopefully you guys can help me.

I have been asked to write a matlab file to show that: f (x) = cos(x²) is monotone decreasing on the interval [o,root(pi/2)]

I know before I start, that I need to used an argument, il call it n, and after the argument has been done, return the upper and lower Riemann sums for f over this interval whilst still having n in equal strips, so I have begun with:

Now I need to set the paramaters, but im quite stuck with it, wonder if any of you can help me?

Regards,
Jason
To show that f(x) is monotone decreasing on the given interval it is sufficient to show that f'(x)<=0 (since the function is differentiable on the interval. This hardly seems something that you would do with Matlab (I suppose you could use the symbolic toolbox to find the derivative ... ).

CB