Let `f(x)=x^3-6x^2+15 x+3` . Then, (a) `f(x)>0` for all `x in R` (b) `f(x)>f(x+1)` for all `x in R` (c) `f(x)` is invertible (d) `f(x)<0` for all `x in R`

Explanation

f(x) is invertible


`f(x)=x^{3}-6 x^{2}+15 x+3 `
`
f^{prime}(x)=3 x^{2}-12 x+15 `
`
=3(x^{2}-4 x+5) `
`
=3(x^{2}-4 x+4+1) `
`
=3(x-2)^{2}+frac{1}{3}>0`


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