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Question

The set of values of a for which the function f(x)=ax33+(a+2)x2+(a1)x+2 possesses a negative point of inflection is

A
(,2)(0,)
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B
(2,0)
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C
ϕ
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D
{4,5}
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Solution

The correct option is A (,2)(0,)
We have,
f(x)=ax33+(a+2)x2+(a1)x+2
f(x)=ax2+2(a+2)x+(a1)
f′′(x)=2ax+2(a+2)=0x=a+2a
For negative point of inflection
a+2a<0
a(,2)(0,)
f′′′(x)=2a0 in the above interval.

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