Jensen’s Inequality & Strictly convex functions

Question

Using the Jensen’s Inequality to show that f(x) = x 2 is strictly convex function.

Answer 1

Jensen's inequality: basically the secant line lies above a convex function

f(x) = x^2 is an upward opening parabola,

connect any 2 points on the parabola & it lies above the parabola

the line between those 2 points is a secant line

2nd deivative f'(x) is always > 0, therefore convex,

or concave up--look down from above & you see a cave shape

others, from outside, view your eye as convex

you see it as concave, from inside, if you could see it

it helps to sketch a graph