GATE 2014 EC (EC3) – Question 36
Find the maximum of $f(x)=2x^3-9x^2+12x-3$ on $0\le x\le3$.
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Correct answer: 5.9 to 6.1
Explanation
Differentiate to get f′=6(x−1)(x−2). Evaluate the endpoints and critical points:f(0)=−3,f(1)=2,f(2)=1,f(3)=6. The largest value is therefore **6**, attained at x=3. The interior local maximum2is not the global maximum.