I have a problem that I am stuck with, if anyone please can give me any hint, that'd be great.(adsbygoogle = window.adsbygoogle || []).push({});

f is a continuous function at the interval [a,b], and f(a) not euqal to f(b).

q and p are two positive integers, and they do not equal zero.

f : [a,b] ---> R

show that :

there is a numbercthat belongs to the interval [a,b] such as:

pf(a) + qf(b) = (p+q)f(c)

----

I only know that you should use the Intermediate Value Theorem, I only learned that this morning and I have no clue how to demonstrate this problem. Thanks for your help...

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Intermediate Value Theorem problem

**Physics Forums | Science Articles, Homework Help, Discussion**