Find the maxima and minima of the function `y=x(x-1)^2,0lt=xlt=2.`

Find all maxima and minima of the function y=x(x-1)^(2) for 0<=x<=2 Also,determine the area bounded by the curve y=x(x-1)^(2) the X -axis and the line x=2 .

Find the local maxima and minima of the function f(x)=x^(3)-2x^(2)+x+6 .

Find the maxima and minima of the following functions : f(x)=x^(2) In x ,

Find the local maxima and minima of the function f(x)=2x^(3)-21x^(2)+36x-20 .

Find the points of maxima and minima of the function f(x)=sin2x+2cos x,x in[0,2] Also comment about the nature of end points.

Find the maxima and minima of the following functions : f(x)=(4x)/(x^(2)+4)

Find the points of local maxima and minima of the function f(x)=x^(2)-4x .

Find the maxima and minima of the following functions : f(x)=root3(2x^(3)+3x^(2)-36x)

Find the maxima and minima of the following functions : f(x)=x^(3)e^(-x)

Find the local maxima and local minima of the functions: (i) f(x) = (sin x - cos x), " When " 0 lt x lt (pi)/(2) (ii) f(x) = (2 cos x + x), " when " 0 lt x lt pi