GATE 2022 AG – Question 36
Which statement describes $(x-2)^2(x+2)^2$?
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Correct answer: (C) Minima at −2 and +2
Explanation
$f=(x^2-4)^2\ge0$ and f=0 at both ±2, so both are minima. Alternatively $f^{\prime}=4x(x^2-4)$ and $f^{\prime\prime}=12x^2-16$ is 32 at ±2. Thus **C**. There is also a local maximum at 0, not at either endpoint named in the alternatives.