The non-negative values of b for which the function 16 x^3 3 -4 b x^2+x has neither maximum nor minimum in the range x 0 is:

Step-by-step solution

Let, f(x)= 16 x^3 3 -4 b x^2+xf(x)=16 x^2-8 b x+1 f(x) is neither maximum nor minimum then aligned f(x) & 0 f(x) & 0 or f(x) 0 aligned For, f(x) 0 aligned & D 0 and a 0 & D =64 b^2-64 0 aligned b^2-1 0 and b is non-negative as b 0 aligned & & b & [0,1] & & 0 & b 1 aligned