MHT CET 2021 Math Solved Paper

Given, function is y=[x(x−2)]2=[x2−2x]2
On differentiating both sides w.r.t. x, we get
‌

dy

dx

‌‌=2(x2−2x)‌

d

dx

(x2−2x)
‌‌=2(x2−2x)(2x−2)=4x(x−2)(x−1)
On putting ‌

dy

dx

=0, we get
4x(x−2)(x−1)=0⇒x=0,1‌ and ‌2
Now, we find interval in which f(x) is strictly increasing or strictly decreasing.Hence, y is strictly increasing in (0,1) and (2,∞). Also, y is a polynomial function, so it continuous at X=0,1 and 2 .
Hence, y is increasing in [0,1]∪[2,∞].