a a- (a) (i) Show that I b b =(a-b)(b-c)(c-a). C (ii) Use the result of (a)(i) to deduce that (1tax) (1tay) (1+az) ( 1 + hx) ( 1 + by ) ( 1 + b= )| = 2( a - b ) ( b - c) (c-a) (x -y) (y-=)(=-x). ( 1 + cx) (1+cy)? (1+c=)? (b) Find all the relative extreme point(s), if any, of the function f (x) = x (1-x) * on (0,1). (c) (i) Let g be a continuous function on R and c be a positive constant. Show that [ x's(x ) dx = , J. x8 (x) dx. (Hint: Let u = x]) (ii) Use the result of (c)(i) to evaluate (x cos(x ) dx