Let f ( x )=5-| x -2| and g ( x )=| x +1|, x R . If f ( x ) attains maximum value at and g(x) attains minimum value at , then _ x - (x-1) (x^2-5 x+6 ) (x^2-6 x+8 ) is equal to

Step-by-step solution

f ( x )=5-| x -2| is maximum at x =2 =2 g ( x )=| x +1| is minimum at x =-1 =-1 Now _ x - (x-1) (x^2-5 x+6 ) (x^2-6 x+8 ) = _ x -(2)(-1) (x-1)(x-2)(x-3) (x-2)(x-4) aligned & = _ x 2 (x-1)(x-3) x-4 & = (2-1)(2-3) 2-4 & = 1 2 aligned