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

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,∞).