The values of and for which all the extrema of the function are positive and the…

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

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

are positive and the minimum is at

x_0=\frac13

are (1) When

a=-2

b<-\frac{11}{27}

, and when

a=3

b<-\frac12

(2) When

a=3

b<-\frac{11}{27}

, and when

a=2

b<-\frac12

(3) When

a=-2

b<-\frac12

, and when

a=3

b<-\frac{11}{27}

(4) None of the above