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

Find a polynomial f(x) of degree 4 which increases in the intervals (-oo,1) and (2,3) and decreases in the intervals (1,2) and (3,oo) and satisfies the condition f(0)=1

Show that f(x)=(1)/(x) is a decreasing function on (0,oo)

y= f(x) is a polynomial function passing through point (0, 1) and which increases in the intervals (1, 2) and (3, oo) and decreases in the intervals (oo,1) and (2, 3). If f(1)= -8, then the range of f(x) is

Show that f(x)=(1)/(x) is decreasing function on (0,oo)

A polynomial function P(x) of degree 5 with leading coefficient one,increases in the interval (-oo,1) and (3,oo) and decreases in the interval (1,3). Given that P(0)=4 and P'(2)=0. Find th value P'(6) .

Let f(x) be a cubic polynomial on R which increases in the interval (-oo,0)uu(1,oo) and decreases in the interval (0,1). If f'(2)=6 and f(2)=2, then the value of tan^(-1)(f(1))+tan^(-1)(f((3)/(2)))+tan^(-1)(f(0)) equals

The function f(x)=(2x^(2)-1)/(x^(4)),x>0 decreases in the interval