The set of value(s) of `a` for which the function `f(x)=(a x^3)/3+(a+2)x^2+(a-1)x+2` possesses a negative point of inflection is (a) `(-oo,-2)uu(0,oo)` (b) `{-4/5}` (c) `(-2,0)` (d) empty set

Options

A. `(-oo,-2)cup(0,oo)`
B. `{-4//5}`
C. `(-2,0)`
D. empty set

Answer

1

Explanation

`f(x) = ax^(2)+2(a+2)x+(a-1)`
`f''(x) =2ax+2(a+2)=0`
Thus `x=(+2)/(a)` which is the point of inflection
Given that we must have `(a+2)/(a) lt or a in (-oo,-2)cup(0,oo)`