# Mean and weighted mean comparison

Dear Friends!
Is weighted mean greater than mean?
Actually i need to prove (c-b)f(a)+(b-a)f(c)>(c-a)f(b) when when f is continuous and strictly increasing in [a,c],where a<b<c.

jbriggs444
Homework Helper
Is what you are trying to prove even true? Can you check against some simple example functions?

Dear friend!Thank You for response!
I have checked it and it comes true for f(x) equal to x square for the positive real domains.

jbriggs444
Homework Helper
Have you checked against the identify function, f(x) = x?

And have you compared the formula in question to linear interpolation?

Stephen Tashi
I have checked it and it comes true for f(x) equal to x square for the positive real domains.

Try $f(x) = \sqrt{x},\ a = 0,\ b = 1,\ c = 9$

Thank You dear friends!
I had realised my mistake and an modifying the question.
Now ingnore first part of question and assume that if in addition it is specified that f'(x) is strictly increasing then the cnjecture seems true.BUT I NEED GENERAL PROOF.

jbriggs444