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

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 (a) [3,oo) (b) [-8,oo) (c) [-7,oo) (d) (-oo,6]

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(x)=0 has four real roots, then the range of values of leading coefficient of polynomial is

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 value of f(2) is

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).

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

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

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

Show that the function f(x)=sin^(4) x+ cos^(4) x (i) is decreasing in the interval [0,pi/4] . (ii) is increasing in the interval [pi/4,pi/2] .

Show that the function f(x) = 1/(1+x^(2)) is increasing function in the interval (- infty, 0] .

Show that the function f(x)=x^(3)+1/(x^(3)) is decreasing function in the interval [-1,1]-{0} .