Monotonic Functions

JuniorNikkie

New member
Joined
Nov 28, 2015
Messages
1
Hi fellows, I need your knowledge for one of my 99 problems!

Here it is:

f and g are continuous and defined in the [a,b] with output in the [a,b], a<>0.
f is monotonically increasing in the [a,b] and g is monotonically decreasing in the [a,b].

Show that there is at least one x in the (a,b) so that: bf(x) + ag(x) = x*(a+b).

 
Hi fellows, I need your knowledge for one of my 99 problems!

Here it is:

f and g are continuous and defined in the [a,b] with output in the [a,b], a<>0.
f is monotonically increasing in the [a,b] and g is monotonically decreasing in the [a,b].

Show that there is at least one x in the (a,b) so that: bf(x) + ag(x) = x*(a+b).

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

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...Before-Posting
 
Top