Question

Find all maxima and minima of the function y = x(x - 1)², 0 ≤ x ≤ 2.

Also, determine the area bounded by the curve y = x(x - 1)², they y -axis and the line x = 2.

Answer 1

Given, y = x (x - 1)² 

=> dy/dx = x.2(x - 1) + ( x - 1)² 

Minimum at x = 1 => y_min = 0

Now, to find the area bounded by the curve y = x (x - 1)² , The y-axis and line x = 2.