answersLogoWhite

0

Consider 2 convex functions g(x) and f(x).

Using property of second derivative test we have:

g(x)'' > 0 and f(x)'' > 0.

We are interested in showing that y(x) = g(x) + f(x) is also convex.

y(x)'' = c*g(x)'' + k*f(x)'', where c and k are positive numbers (where is no convex function those coeficients after diferentiation will give you negative numbers).

Because c, g(x)'', k, f(x)'' are > 0 , we get y(x)'' also >0, hence y(x) is a convex function.

User Avatar

Wiki User

17y ago

Still curious? Ask our experts.

Chat with our AI personalities

BlakeBlake
As your older brother, I've been where you are—maybe not exactly, but close enough.
Chat with Blake
SteveSteve
Knowledge is a journey, you know? We'll get there.
Chat with Steve
JudyJudy
Simplicity is my specialty.
Chat with Judy

Add your answer:

Earn +20 pts
Q: Show that sum of two convex functions is convex.?
Write your answer...
Submit
Still have questions?
magnify glass
imp