Cosider the function `f(x)=|{:(x^(3),sin x,cos x),(6,-1,0),(p,p^(2),p^(3)):}|`, where p is a constant.
What is the value of p for which f''(0) = 0 ?

Options

A. `-(1)/(6) or 0`
B. `-1 or 0`
C. `-(1)/(6) or 1`
D. `-1 or 1`

Answer

A

Explanation

`f''(x)=|(6x,-sinx,-cosx),(6,-1,0),(p,p^(2),p^(3))|`
`f''(0)=|(0,0,-cos0),(6,-1,0),(p,p^(2),p^(3))|`
`=-1(6p^(2)+p)`
`f''(0)=0`
`-(6p^(2)+p)=0`
`p(6p+1)=0`
`p=0 or p=-(1)/(6)`