Home › Previous year questions › GATE 2020 BT › Question 60GATE 2020 BT – Question 60 Engineering Mathematics · Calculus: Limits, continuity, differentiability, partial derivatives, maxima and minima · 2 marks · Numerical answer
For $f(X)=4X-X^2$, at which X is f maximized?
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Show answer and explanation Correct answer: 2 to 2
Explanation Differentiate: $f\prime(X)=4-2X$, which vanishes at X = 2. The second derivative is −2, so the stationary point is a strict maximum. Equivalently $f(X)=4-(X-2)^2\le4$, proving it is the global maximum. Thus X = 2.
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