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.

Statement 1: The function f(x)=x In x is increasing in (1/e ,oo) Statement 2: If both f(x)a n dg(x) are increasing in (a , b),t h e nf(x)g(x) must be increasing in (a,b).

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)

Statement 1: Both f(x)=2cos x+3sinxa n dg(x)=sin^(-1)x/(sqrt(13))-tan^(-1)3/2 are increasing in (0, pi /2) Statement 2: If f(x) is increasing, then its inverse is also increasing.

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

Separate the intervals of monotonocity of the function: f(x)=3x^4-8x^3-6x^2+24 x+7

Consider the function f:(-oo,oo)vec(-oo,oo) defined by f(x)=(x^2+a)/(x^2+a),a >0, which of the following is not true? maximum value of f is not attained even though f is bounded. f(x) is increasing on (0,oo) and has minimum at ,=0 f(x) is decreasing on (-oo,0) and has minimum at x=0. f(x) is increasing on (-oo,oo) and has neither a local maximum nor a local minimum at x=0.

Prove that f(x) = x^(2) -6x + 3 is strictly increasing in (3, oo)

For the cubic function f(x)=2x^3+9x^2+12 x+1, which one of the following statement/statements hold good? f(x) is non-monotonic. f(x) increases in (-oo,-2)uu(-1,oo) and decreases in (-2,-1) f: RvecR is bijective. Inflection point occurs at x=-3/2dot

Let f(x) be a function such that f(x)=(log)_(1/2)[(log)_3(sinx+a]dot If f(x) is decreasing for all real values of x , then a in (1,4) (b) a in (4,oo) a in (2,3) (d) a in (2,oo)

If f(x)=xe^(x(x−1)) , then f(x) is (a) increasing on [−1/2,1] (b) decreasing on R (c) increasing on R (d) decreasing on [−1/2,1]