Let `f` be the function `f(x)=cosx-(1-(x^2)/2)dot` Then (a) `f(x)` is an increasing function in `(0,oo)` (b) `f(x)` is a decreasing function in `(-oo,oo)` (c) `f(x)` is an increasing function in `(-oo,oo)` (d) `f(x)` is a decreasing function in `(-oo,0)`

The function f(x)=(sinx+cosx) is an increasing function in

Let f: R->R be a differentiable function for all values of x and has the property that f(x)a n df^(prime)(x) has opposite signs for all value of xdot Then, (a) f(x) is an increasing function (b) f(x) is an decreasing function (c) f^2(x) is an decreasing function (d) |f(x)| is an increasing function

(i) The function f(x)=x^(3) is decreasing in (-oo, oo) (ii) The function f(x)=x^(4) is increasing in (-oo, 0) , then-

The function defined by f(x)=(x+2)e^(-x) is (a)decreasing for all x (b)decreasing in (-oo,-1) and increasing in (-1,oo) (c)increasing for all x (d)decreasing in (-1,oo) and increasing in (-oo,-1)

Let f(x)=xsqrt(4a x-x^2),(a >0)dot Then f(x) is (a). increasing in (0,3a) decreasing in (3a, 4a) (b). increasing in (a, 4a) decreasing in (5a ,oo) (c). increasing in (0,4a) (d). none of these

Show that the function f(x)=(3x+5)/(x+2) is strictly monotonic increasing in [0, oo) .

The function f(x) = "max"{(1-x), (1+x), 2}, x in (-oo, oo) is

Statement 1: The function f(x)=x^4-8x^3+22 x^2-24 x+21 is decreasing for every x in (-oo,1)uu(2,3) Statement 2: f(x) is increasing for x in (1,2)uu(3,oo) and has no point of inflection.

What is the value of b for which the function f(x)=sinx-bx+c is decreasing in the interval (-oo, oo) ?

Let f(x) be an decreasing function defined on (0,oo) . If f(3a^2-4a+1)gtf(2a^2+a+1) and the range of a is (o,K/3)uu(K,K+4) , find K