A function is matched below against an interval where it is supposed to be increasing. Which of the following parts is incorrectly matched? Interval, Function [2, `oo)` , `2x^3-3x^2-12 x+6` `(-oo,oo)` , `x^3=3x^2+3x+3` `(-oo-4)` , `x^3+6x^2+6` `(-oo,1/3)` , `3x^2-2x+1`

Options

A. `{:("Function","Interval"),(x^(3)+6x^(2)+6, (-oo,-4)):}`
B. `{:("Function","Interval"),(3x^(2)-2x+1, (-oo,1/3)):}`
C. `{:("Function","Interval"),(2x^(3)-3x^(2)-12x+6,[2,oo)):}`
D. `{:("Function","Interval"),(x^(3)-3x^(2)+3x+3,(-oo,oo)):}`

Answer

B

Explanation

Let `f(x)=x^(3)+6x^(2)+6`……………..i
`impliesf'(x)=3x^(2)+12x=3x(x+4)`
For `f(x)` to be increasing `f'(x)gt0`
`implies x epsilon(-oo,-4)uu(0,oo)`

b. Let `f(x)=3x^(2()-2x+1impliesf'(x)=6x-2`
For `f(x)` to be increasing `f'(x)gt0`,
`implies 6x-2thetaimpliesx gt1/3`
`implies x epsilon(1/3,oo)`
Hence incorrectly mathced.