# True or false

## Homework Statement

1. if a function is twice continuously differentiable with f''(x) >= 0 for all real values of x then

(f(-x) + f(x))/2 >= f(0) ?

2. if a function is twice continuously differentiable with f''(x) >= 0 for all real values of x then
tf(x) + (1-t)f(y) >= f(tx+(1-t)y)
for all real values of x and y and for 0<=t<=1

I am really confused with these types of questions and to how to attempt them in my exam.

Thanks

jbunniii
Homework Helper
Gold Member
If $f''(x) \geq 0$ for all real x, then what kind of function is f?

convex?

jbunniii
Homework Helper
Gold Member
convex?

Yes. Now what's the definition of a convex function?

No idea?

No idea?

Look it up?

when i try and look it up it just keeps telling me exactly what part 2 says, i know its true but i need to prove it you see.

jbunniii