GATE DA 2026 Q27: Roots and extrema of x³ − 3x² + 2 on (−1, 3]

Let $f(x) = x^3 - 3x^2 + 2$ be a function defined on $(-1, 3]$ .

Which of the following statements is/are correct?

Try it: multiple select: one or more correct options

Select all correct options. No negative marking, no partial marks.

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Answer: B, D (official GATE 2026 final answer key)

Concept used: Critical points from $f'(x) = 0$ , and comparing with the value at the closed end of the interval.

First step: $f'(x) = 3x(x - 2)$ ; compare $f(0) = 2$ , $f(2) = -2$ and the endpoint $f(3) = 2$ , and check $f(1)$ .

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Source: official GATE 2026 DA question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key