How can there be a function with a second derivative greater than zero

[Aerosion]

Homework Statement

yet is approaching negative infiniti?

We were discussing a question that went "suppose f double prime (x)>0 and x ranges from negative infiniti to infiniti, and f(a)=0. Prove or disprove that f(x) is bounded below."

The man said that e^-x - x had a second derivative greater than zero, which i understand, but then how does it go to negative infiniti? I don't understand that, it should go to positive infiniti, right?

Homework Equations

The Attempt at a Solution

 

[Dick]

If f(x)=exp(-x)-x, f(x) does go to positive infinity as x->-infinity. What happens if x->+infinity?