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.
Still curious? Ask our experts.
Chat with our AI personalities
Ross
Fran
ViviAdd your answer:
Earn +20 pts
What is the name of a quadrilateral with two right angles?
It is a convex quadrilateral, as the remaining angles could be any two angles with a sum of 180 degrees.
Are the sum of two periodic functions always periodic?
yes
Is the graph of two continuous function is always continue?
Well, it sounds like a plausible statement, and maybe it would be true . But we haveno idea what the graph of two functions is.Perhaps you could graph the sum of two functions, or the difference of two functions,or their product, or their quotient. We believe that if the original two functions areboth continuous, then their sum and difference would also be continuous, but theirproduct and their quotient might not necessarily be continuous. However, we stilldon't know what the "graph of two functions" is.
What is differentiale convex and non-convex?
Take any two points on or inside a body. If every point on the straight line joining the two points lies within the shape, then it is convex. If not, it is non-convex.
What are The measure of an exterior angle of a triangle is greater than the sum of the measures of the two opposite interior angles?
It is an indication of an error, or the fact that the triangle is not in the Euclidean plane but on a convex surface.
