For the cubic function `f(x)=2x^3+9x^2+12 x+1,` which one of the following statement/statements hold good? `1`. `f(x)` is non-monotonic. `2`. `f(x)` increases in `(-oo,-2)uu(-1,oo)` and decreases in `(-2,-1)` `3`. `f: RvecR` is bijective. `4`. Inflection point occurs at `x=-3/2dot`

The function f(x)= 4x^2+2x+1 is increasing for?

Find the interval in which f(x)=2x^3+3x^2-12x+1 is increasing.

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

Which of the following hold(s) good for the function f(x)=2x-3x^(2/3) AAx in R ?

f(x)=(x-2)|x-3| is monotonically increasing in (a) (-oo,5/2)uu(3,oo) (b) (5/2,oo) (c) (2,oo) (d) (-oo,3)

Find the interval in which f(x)= 4x^3+3x^2+2x+1 is increasing.

f(x)=|x^2-3|x|+2|dot Then which of the following is/are true f^(prime)(x)=2x-3 for x in (0,1)uu(2,oo) f^(prime)(x)=2x+3 for x in (-oo,-2)uu(-1,0) f^(prime)(x)=-2x-3 for x in (-2,-1) None of these

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

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.

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