Given function f(x)=x√kx−x2=√kx3−x4 Differentiating w. r. t. x, f′(x)=
(3kx2−4x3)
2√kx3−x4
≥0 for x∈[0,3][∵f(x) is increasing in [0,3]] ⇒3k−4x≥0⇒3k≥4x i.e., 3k≥4x for x∈[0,3] ∴k≥4 i.e., m=4 Putting k=4 in the function, f(x)=x√4x−x2 For max. value, f′(x)=0 i.e.