GATE 2024 ES – Question 32

Mathematics Foundation · Calculus · 1 mark · Numerical answer

$f(x)=x^3-4.5x^2-12x$ has a local maximum at what integer x in[−2,2]?

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Correct answer: -1 to -1

Explanation

Differentiate: $f^{\prime}=3x^2-9x-12=3(x-4)(x+1)$. Critical points are4 and−1; only−1 lies in the interval. The second derivative $f^{\prime\prime}=6x-9$ equals−15 at−1,so it is a local maximum. Answer **−1**.

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