5. Prove or disprove each of the following. State clearly Whether it is true or false. (a) (4 points) Let f : R2 > R be a continuous function having at least one point of local minimum and at least one point of local maximum. Then there must be a point of local minimum a and a point of local maximum b such that f(a) S f (b) (b) (4 points) Let f: [0,1] x [0,1] > R be a continuous function. Dene g : [0,1] x [0,1] > R by a: 9($,y)=LyL f(s,t)d3dt. Then for any 0