it is given that
hint: prove first that is a convex
on this region
reminder: function f(t) is called convex on some region if for every b,a
i know from calc1 that a function is convex if its second derivative is negative or something (i am not sure)
i dont know
how to prove that is negative
its pure parametric thing
Please do not take this as an offense, but from this and the other thread you started and the responses I got there from you, I think you should really begin to worry about learning SERIOUSLY the very basic facts of the subjects you're asking about. It seems like you don't have the slightest idea what you're talking about, you're completely lost... and yet you're the one who sent the question!
I, for one, am not here to teach from scratch a whole subject to anyone so that he/she will be able to understand solutions to his/her own questions.
you better study the basics, understand definitions and notation, and THEN, if you get stuck somewhere, you ask. That's, btw, the only way to learn something in mathematics, imo.
Ps. The answer to this thread's question is already in my prior messages...and no: the given in your question is not to explain convexity: you need it to approach the question and eventually reach a solution, and also p is given and from where t is taken...