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`

Options

A. f(x) is non monotonic
B. f(x) increses in `(-oo,-2)cup(-1,oo)` and decreases in (-2,-1)
C. f:R `rarr` R is objective
D. O inflection point occurs at x =-`3//2`

Answer

1,2,4

Explanation

`f(X)=2x^(3)+9x^(2)+12x+1`
`f(x)=6[x^(2)+3x+2]`
`=6(x+2)(x+1)`
`f(X)lt0forxin(-2,-1)` where f(X) decrease
`f(X)gt0 for x in (-oo,-2)cup(-1,oo)` where f(X) increase
`f(X)gt0 for x in (-oo,2)cup(-1,oo)` where f(x) increase
f(x)=6(2x+3)=0
Thus `x=-3//2` is the point of inflection

From the graph f is many one hence it is not bijective