# Math Help - Prove Convexity Using Formal Definition

1. ## Prove Convexity Using Formal Definition

How can I prove that: f (x) =∏·ln(x) + √x on domain (0, 15) is strictly concave using the formal definition of concavity?

Can someone help me get started? Thanks!

Regards,
Esther

2. Yes, start by stating the "formal definition of concavity"!

(Does the problem really say just "concave" and not "concave upward" or "concave downward"?)

3. OK - the formal definition is:

f(ax1+(1-a)x2)>af(x1)+(1-a)f(x2)

but I just don't know where to go from here. I can't even find similar problems with a google search! Thanks!

Also, the problem just says concave. I assume concave=concave downward and convex=concave upward, right?

Regards,
Esther

Originally Posted by HallsofIvy
Yes, start by stating the "formal definition of concavity"!

(Does the problem really say just "concave" and not "concave upward" or "concave downward"?)