Exams › JEE Main › Maths
A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is incorrectly matched? Interval (a) (-∞, ∞) — x^3 - 3x^2 + 3x + 3 (b) [2, ∞) — 2x^3 - 3x^2 - 12x + 6 (c) (-∞, 1/3] — 3x^2 - 2x + 1 (d) (-∞, -4) — x^3 + 6x^2 + 6
- (a) (-∞, ∞) — x^3 - 3x^2 + 3x + 3
- (b) [2, ∞) — 2x^3 - 3x^2 - 12x + 6
- (c) (-∞, 1/3] — 3x^2 - 2x + 1
- (d) (-∞, -4) — x^3 + 6x^2 + 6
Correct answer: (b) [2, ∞) — 2x^3 - 3x^2 - 12x + 6
Solution
Option (b) is incorrect because the function 2x^3 - 3x^2 - 12x + 6 has a derivative that indicates it is not increasing over the interval [2, ∞), as it has critical points and changes in sign within that range.
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