The function f(x)=x2(x−2)2
Decreases on (0, 1) ∪ (2, ∞)
Increase on (−∞, 0) ∪ (1, 2)
Has a local maximum value 0
Has local maximum value 1
f(x)=x2(x−2)2
f′(x)=2x(x−2)2+2x2+(x−2)=4x(x−2)(x−1) f′(x)≥0 for x ε[0,1]∪[2,∞]f′(x)≤0 for x ε(−∞,0)∪[1,2]