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 )

Show that the function f(x)=x^(2) is a strictly increasing function on (0,oo).

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)

Show that the function f(x)=x^2 is strictly increasing function on (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)

Show that the function f(x)=x^2 is a strictly decreasing function on (-oo,\ 0) .

Without using the derivative, show that the function f(x)=|x| is (a) strictly increasing in (0,\ oo) (b) strictly decreasing in (-oo,\ 0)

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)

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)

If the function f(x)=2x^2-k x+5 is increasing on [1,\ 2] , then k lies in the interval (a) (-oo,\ 4) (b) (4,\ oo) (c) (-oo,\ 8) (d) (8,\ oo)