# Thread: Using Taylor Polynoms for solving general problems

1. ## Using Taylor Polynoms for solving general problems

Let f be derivative twice in (a,b) , and $\forall x \in (a,b) : f''(x) \geq 0$
Prove / Give a negative example:
$\forall c,d \in (a,b) : f(\frac{c+d}{2}) \leq \frac{f(c)+f(d)}{2}$ .

If that's a proof, then I'll have to use a Taylor Series to explain f(x), but how do I show that one side is smaller than the other?

Thanks!

2. Does anybody know how to solve this?

3. ## suggestion

Let f be derivative twice in (a,b) , and $\forall x \in (a,b) : f''(x) \geq 0$
Prove / Give a negative example:
$\forall c,d \in (a,b) : f(\frac{c+d}{2}) \leq \frac{f(c)+f(d)}{2}$ .

If that's a proof, then I'll have to use a Taylor Series to explain f(x), but how do I show that one side is smaller than the other?

Thanks!
what would happen if we expand f(c) and f(d) also using taylor's series???then sum the terms.

4. Originally Posted by Pulock2009
what would happen if we expand f(c) and f(d) also using taylor's series???then sum the terms.
Hmm, but around which point? I tried to expand f(0.5(c+d)) one time around c, and one time around d, but it didn't really work...