Using Jensen's inequality for the function ,
Consider the three points on the curve and . When joined they form a triangle which obviously lies below the curve .Now centroid of this triangle is inside the triangle and thus centroid is also below the curve.
Co-ordinates of centroid= .
The corresponding point on the curve with the same -coordinate will be
Since this point is above the centroid .Therefore,
Hey,you can try plotting and draw a triangle and check for yourself