Hi, I am learning differential equations, and came across concept of maximization.

If c : [a, b] → R is uniformly bounded and x ∈ C^2 ([a, b]) satisfies the diﬀerential inequality x'' + c(t)x' > 0 on [a, b].

How does this show that the maximum value of x should occur at end–points of the interval?

Can someone please help me on this?

Regards, Salil

Maximum principles for differential equations. – Denis Serre Sep 23 '10 at 7:11