Problem

Problem

The values of

a

and

b

for which all the extrema of the function,

f(x) = a^2x^3 - 0.5ax^2 - 2x - b

, is positive and the minimum is at the point

x_0 = \frac{1}{3}

, are a. when

a = -2 \Rightarrow b < -\frac{11}{27}

and when

a = 3 \Rightarrow b < -\frac{1}{2}

b. when

a = 3 \Rightarrow b < -\frac{11}{27}

and when

a = 2 \Rightarrow b < -\frac{1}{2}

c. when

a = -2 \Rightarrow b < -\frac{1}{2}

and when

a = 3 \Rightarrow b < -\frac{11}{27}

d. None of the above

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