Help neede( I will rate Lifesaver)

Is this statement ture or false explain why.

If  f (x, y) has exactly two critical points, they can't both be local maxima.
ONE IMPORTANT POINT IS MISSING
IS THE FUNCTION CONTINUOUS BETWEEN THOSE 2 CRITICAL POINTS.
CASE 1
CONTINUOUS ...SEE SKETCH BELOW [FOR CONVENIENCE DRAWING X-Y DIAGRAM

K AND M ARE  2 CRITICAL POINTS REPRESENTING 2 LOCAL MAXIMAS.
THERE HAS TO BE ONE LOCAL MINIMA BETWEEN THEM IF THE FUNCTION IS CONTINUOUS
HENCE GIVEN STATEMENT IS TRUE.
CASE 2
FUNCTION IS DISCONTINUOUS BETWEEN THE 2 CRITICAL POINTS
SEE SKETCH BELOW


K AND M ARE  2 CRITICAL POINTS REPRESENTING 2 LOCAL MAXIMAS.
THERE NEED NOT BE ONE LOCAL MINIMA BETWEEN THEM IF THE FUNCTION IS DISCONTINUOUS
HENCE GIVEN STATEMENT IS NOT TRUE IN THIS CASE