K
Kelci C
Guest
Hey, I really need some help figuring these out. We're starting our integral unit and I have an exam coming up shortly. If you can show me the steps on solving this, it would help a lot. Thanks.
1. Suppose that f is concave upward and differentiable on (a,b). Let x < y in [a,b] and p be in (0,1), show that:
f(p*x + (1-p)*y) < p*f(x) + (1-p)*f
What is the analogous inequality for a differentiable concave downward function?
Thanks
1. Suppose that f is concave upward and differentiable on (a,b). Let x < y in [a,b] and p be in (0,1), show that:
f(p*x + (1-p)*y) < p*f(x) + (1-p)*f
What is the analogous inequality for a differentiable concave downward function?
Thanks