Question

Find the values of x for which y=[x(x-2)]² is an increasing function.

Answer 1

We have,

The points x = 0, x = 1, and x = 2 divide the real line into four disjoint intervals i.e.,

∴ y is strictly increasing in intervals (0, 1) and (2, ∞).
y is strictly increasing for 0 < x < 1 and x > 2.