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GATE 2026 AE – Question 51

Engineering Mathematics · Calculus: Limits, continuity, differentiability, chain rule, maxima and minima, integration · 2 marks · Numerical answer

The minimum value of the function $f(x) = |x| + |2x + 3|$ for real $x$ is ________ (rounded off to 1 decimal place).

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Correct answer: 1.49 to 1.51

Explanation

For $x < -1.5$: $f = -3x - 3$, which falls as $x$ rises. For $-1.5 \le x \le 0$: $f = x + 3$, which rises. For $x > 0$: $f = 3x + 3$. The minimum is at $x = -1.5$: $f = 1.5 + 0 = 1.5$.