1. The problem statement, all variables and given/known data f(x)=x[ax-x^2]^ (1/2) for a>0 Then,f(x) A)increases on (3a/4 , a) B)decreases on (0, 3a/4) C)both A,B D)None of these 2. Relevant equations differentiation chain rule f(x) is said to be increasing in (a,b) if it's derivative is positive and decreasing if it's derivative is negative for all x b/w a and b 3. The attempt at a solution First af all,I found the domain of the given function which came out to be [0,a] Now,the derivative of the function is: (3ax-4x^2)/ [(4ax-4x^2)^1/2] Now,the term in the denominator being inside square root is always positive,so we only need to deal with the numerator. Which is: x(3a-4x) Now,due to it's domain x is also positive Therefore the first term of the numerator is also positive,so it all comes down to the second term.. (3a-4x) which is positive(and hence the function increasing) for x b/w 0 and 3a/4 ,and negative for the rest.So,the corresponding option comes out to be D. But,the answer given is C. If anybody can point out where I am going wrong (or if the answer given is wrong,whichever),it qould be very helpful..