Function `f(x)=x^3-27 x+5` is monotonically increasing when (a) `x<-3` (b) `|x|>3` (c) `xlt=-3` (d) `|x|geq3`

Explanation

Answeris D)
`
f(x)=x^{3}-27 x+5` monotonically increasing
`
f^{prime}(x)=3 x^{2}-27`
`
f^{prime}(x)>0 `for monotically increasing
`
Rightarrow 3 {x}^{2}-27>0`
`
x^{2}-9>0`
`
(x+3)(x-3)>0`

Drawing its sign scheme, we have
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