GATE 2016 EC (EC2) – Question 13
As $x$ varies from −1 to +3, which describes the behaviour of $f(x)=x^3-3x^2+1$?
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Correct answer: (B) increases, then decreases and increases again
Explanation
Differentiate: $f\prime(x)=3x(x-2)$. It is positive on (−1,0), negative on (0,2), and positive on (2,3).
Therefore f first increases to its local maximum at x=0, then decreases to its local minimum at x=2, then increases again. The correct sequence is **B**.