`f(x)=(x-2)|x-3|` is monotonically increasing in (a)`(-oo,5/2)uu(3,oo)` (b) `(5/2,oo)` (c)`(2,oo)` (d) `(-oo,3)`

The differentiable function y= f(x) has a property that the chord joining any two points A (x _(1), f (x_(1)) and B (x_(2), f(x _(2))) always intersects y-axis at (0,2 x _(1) x _(2)). Given that f (1) =-1. then: The largest interval in which y =f (x) is monotonically increasing, is : (a) (-oo,(1)/(2)] (b) [(-1)/(2),oo) (c) (-oo, (1)/(4)] (d) [(-1)/(4), oo)

The interval in which the function f given by f(x) = x^2 e^(-x) is strictly increasing is (a) ( -oo , oo ) (b) ( -oo , 0 ) (c) ( 2 , oo ) (d) ( 0 , 2 )

the interval in which the function f given by f(x) = x^2 e^(-x) is strictly increasing, is (a) ( -(oo) , (oo) ) (b) ( -(oo) , 0 ) (c) ( 2 , (oo) ) (d) ( 0 , 2 )

the interval in which the function f given by f(x) = x^2 e^(-x) is strictly increasing, is (a) ( -(oo) , (oo) ) (b) ( -(oo) , 0 ) (c) ( 2 , (oo) ) (d) ( 0 , 2 )

If f(x)=int_(0)^(x)log_(0.5)((2t-8)/(t-2))dt , then the interval in which f(x) is increasing is (a) (-oo,2)uu(6,oo) (b) (4,6) (c) (-oo,2)uu(4,oo) (d) (2,6)

The value of a for which the function f(x)=(4a-3)(x+log5)+2(a-7)cot(x/2)sin^2(x/2) does not possess critical points is (a) (-oo,-4/3) (b) (-oo,-1) (c) [1,oo) (d) (2,oo)

The function f(x)=cot^(-1)x+x increases in the interval (a) (1,\ oo) (b) (-1,\ oo) (c) (-oo,\ oo) (d) (0,\ oo)

The interval in which y=x^2""e^(-x) is increasing is (A) (-oo,""""oo) (B) ( 2, 0) (C) (2,""""oo) (D) (0, 2)

f(x)=ln(lnx) (x>1) is increasing in a) (0,1) b) (1, oo) c) (0,2) d) (-oo, 1)

If the function f(x)=x^2-k x+5 is increasing on [2,\ 4] , then (a) k in (2,\ oo) (b) k in (-oo,\ 2) (c) k in (4,\ oo) (d) k in (-oo,\ 4)