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

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- November 9th 2009, 08:20 PMsyokProve 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 - November 10th 2009, 04:48 AMHallsofIvy
Yes, start by stating the "formal definition of concavity"!

(Does the problem really say just "concave" and not "concave upward" or "concave downward"?) - November 10th 2009, 09:37 AMsyok
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