Let `f(x) =x^3+1/x^3` ,lft the intervals in which f(x) increases are `( oo,a]` and `[b,oo)` then min(b-a) is =

Show that f(x)=1/(1+x^2) decreases in the interval [0,oo) and increases in the interval (-oo,0]dot

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)

Let f(x)=x^4-4x^3+6x^2-4x+1. Then, (a) f increase on [1,oo] (b) f decreases on [1,oo] (c) f has a minimum at x=1 (d) f has neither maximum nor minimum

Let f(x)=x^4-4x^3+6x^2-4x+1. Then, (a) f increase on [1,oo] (b) f decreases on [1,oo] (c) f has a minimum at x=1 (d) f has neither maximum nor minimum

Let f(x) = cos x - (1 - (x^(2))/(2)) then f(x) is increasing in the interval a) (-oo, 1] b) [0, oo) c) (-oo, -1] d) (-oo, oo)

Show that f(x)=1/(1+x^2) decreases in the interval [0,\ oo) and increases in the interval (-oo,\ 0] .

If e^x+e^(f(x))=e , then the range of f(x) is (-oo,1] (b) (-oo,1) (1, oo) (d) [1,oo)

Show that f(x)=(1)/(1+x^(2)) decreases in the interval [0,oo) and increases in the interval (-oo,0].

Show that f(x)=(1)/(1+x^(2)) decreases in the interval [0,oo) and increases in the interval (-oo,0].

If f(x)=2x+cot^(-1)x+log(sqrt(1+x^2)-x) then f(x) (a)increase in (0,oo) (b)decrease in [0,oo] (c)neither increases nor decreases in [0,oo] (d)increase in (-oo,oo)