The set of $$value(s)$$ of a for which the function $$f(x)=ax33+(a+2)x2+(a$$−$$1)x+2$$ possesses a negative point of inflection is

Correct option is 1(−∞,−2)∪(0,∞)

Questions

The set of value(s) of a for which the function $f (x) = \frac{{ax}^{3}}{3} + (a + 2) x^{2} + (a - 1) x + 2$ possesses a negative point of inflection is

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(−∞,−2)∪(0,∞)

{−4/5}

(−2,0)

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detailed solution

Correct option is A

f′(x)=ax2+2(a+2)x+(a−1)f′′(x)=2ax+2(a+2)=0Thus, x=−a+2a which is the point of inflectionGiven that we must have a+2a<0 or a∈(−∞,−2)∪(0,∞).

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The set of value(s) of a for which the function f(x)=ax33+(a+2)x2+(a−1)x+2 possesses a negative point of inflection is

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The set of value(s) of a for which the function $f (x) = \frac{{ax}^{3}}{3} + (a + 2) x^{2} + (a - 1) x + 2$ possesses a negative point of inflection is