Monotonic Functions

[JuniorNikkie]

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).

 

[Deleted member 4993]

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?

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