Hi. I need help with this:

Show that if f is concave up on [a,b] and if there exists numbers

$\displaystyle a\leq x_{j}\leq b$

$\displaystyle 1\leq j\leq p$

and

$\displaystyle 0\leq \lambda _{j}\leq 1$

$\displaystyle 1\leq j\leq p$

such that

$\displaystyle \sum \lambda _{j}=1$

then

$\displaystyle f(\sum ^{p}_{j=1}\lambda _{j}x_{j})\leq \sum ^{p}_{j=1}\lambda _{j}f(x_{j})$

True for j=2, prove for j=p+1