Concept:Use differentiation to find the local maximum of f(x)=x2/3+(x−2)2/3.Explanation:Let f(x)=x2/3+(x−2)2/3.Differentiate:f′(x)=32x−1/3+32(x−2)−1/3Set f′(x)=0:x−1/3+(x−2)−1/3=0This gives:(x−2)1/3=−x1/3Cubing both sides:x−2=−x⇒2x=2⇒x=1Find the second derivative:f′′(x)=−92x−4/3−92(x−2)−4/3At x=1, both terms are negative, so f′′(1)<0, confirming a maximum.Substitute x=1:f(1)=12/3+(−1)2/3=1+1=2Note: As ∣x∣→∞, f(x)→∞, so this is the local maximum value, which matches the given options.Answer:The maximum value is 2 (Option B).