Let `f(x_1,x_2,x_3,x_4)=x_1^2+x_2^2+x_3^2+x_4^2-2(x_1+x_2+x_3+x_4)+10`
and `x_1,x_3 in [-1,2]` and `x_2,x_4 in [1,4]` then the maximum value of f is

Let f(x)=min{4x+1,x+2,-2x+4}. then the maximum value of f(x) is

Let f(x)=|[1+sin ^2 x, cos ^2 x , 4 sin 2 x],[ sin ^2 x ,1+cos ^2 x , 4 sin 2 x],[ sin ^2 x , cos ^2 x , 1+4 sin 2 x]| , the maximum value of f(x) is

Let f(x)=|x^2-3x-4|,-1lt=xlt=4 Then f(x) is monotonically increasing in [-1,3/2] f(x) monotonically decreasing in (3/2,4) the maximum value of f(x)i s(25)/4 the minimum value of f(x) is 0

Let f(x)=|x^2-3x-4|,-1lt=xlt=4 Then f(x) is monotonically increasing in [-1,3/2] f(x) monotonically decreasing in (3/2,4) the maximum value of f(x)i s(25)/4 the minimum value of f(x) is 0

If (x_i , 1/x_i), i = 1, 2, 3, 4 are four distinct points on a circle, then (A) x_1 x_2 = x_3 x_4 (B) x_1 x_2 x_3 x_4 = 1 (C) x_1 + x_2 + x_3 + x_4 = 1 (D) 1/x_1 + 1/x_2 + 1/x_3 + 1/x_4 = 1

If (x_i , 1/x_i), i = 1, 2, 3, 4 are four distinct points on a circle, then (A) x_1 x_2 = x_3 x_4 (B) x_1 x_2 x_3 x_4 = 1 (C) x_1 + x_2 + x_3 + x_4 = 1 (D) 1/x_1 + 1/x_2 + 1/x_3 + 1/x_4 = 1

The function f(x) = x^3 - 6x^2 + ax + b is such that f(2) = f(4) = 0 . Consider two statements. (S1) there exists x_1, x_2 in (2,4), x_1 lt x_2 , such that f' (x_1) = - 1 and f'(x_2) = 0 . (S2) there exists x_3, x_4 in (2, 4), x_3 lt x_4 , such that f is decreasing in (2 , x_4) , increasing in (x_4,4) and 2f'(x_3) = sqrt3 f(x_4) .

The function f(x) = x^3 - 6x^2 + ax + b is such that f(2) = f(4) = 0 . Consider two statements. (S1) there exists x_1, x_2 in (2,4), x_1 lt x_2 , such that f' (x_1) = - 1 and f'(x_2) = 0 . (S2) there exists x_3, x_4 in (2, 4), x_3 lt x_4 , such that f is decreasing in (2 , x_4) , increasing in (x_4,4) and 2f'(x_3) = sqrt3 f(x_4) .