A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is incorrectly matched? - Mathematics MCQ AIEEE 2026 | ExamTest.live | ExamTest.live

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A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is incorrectly matched?

A $(- \infty, \infty) for x^{3} - 3 x^{2} + 3 x + 3$
B $[2, \infty) for 2 x^{3} - 3 x^{2} - 12 x + 6$
C $(- \infty, 1/3] for 3 x^{2} - 2 x + 1$
D $(- \infty, - 4] for x^{3} + 6 x^{2} + 6$

Solution & Step-by-step Explanation

A function f (x) is increasing if f^{'} (x) \geq 0 .Check Option C: f (x) = 3 x^{2} - 2 x + 1 f^{'} (x) = 6 x - 2 .For the function to be increasing: 6 x - 2 \geq 0 ⟹ x \geq 1/3 .The interval should be [1/3, \infty) .The given interval is (- \infty, 1/3], which is where the function is actually decreasing.Thus, Option C is incorrectly matched.

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A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is incorrectly matched?

A

(- \infty, \infty) for x^{3} - 3 x^{2} + 3 x + 3

B

[2, \infty) for 2 x^{3} - 3 x^{2} - 12 x + 6

C

(- \infty, 1/3] for 3 x^{2} - 2 x + 1

D

(- \infty, - 4] for x^{3} + 6 x^{2} + 6

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Calculus Increasing and Decreasing Functions

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