Consider f(x) = 2x^3 - 9x^2 + 12x + 6 . Then: - Mathematics MCQ Mathematics Mock Test - 11 2026 | ExamTest.live

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Consider f (x) = 2 x^{3} - 9 x^{2} + 12 x + 6 . Then:

Solution & Step-by-step Explanation

Find critical points by f^{'} (x) = 0 : f^{'} (x) = 6 x^{2} - 18 x + 12 = 6 (x^{2} - 3 x + 2) = 6 (x - 1) (x - 2) .Critical points are x = 1 and x = 2 .Evaluate f (x) at x = 1, x = 2 and endpoint x = 3 : f (1) = 2 (1)^{3} - 9 (1)^{2} + 12 (1) + 6 = 2 - 9 + 12 + 6 = 11 . f (2) = 2 (2)^{3} - 9 (2)^{2} + 12 (2) + 6 = 16 - 36 + 24 + 6 = 10 . f (3) = 2 (3)^{3} - 9 (3)^{2} + 12 (3) + 6 = 54 - 81 + 36 + 6 = 15 .In the interval [1, 3] :Absolute Maximum = 15 (at x = 3).Absolute Minimum = 10 (at x = 2).Option A is correct.

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Consider f (x) = 2 x^{3} - 9 x^{2} + 12 x + 6 . Then:

The absolute maximum of the function is 15 in the interval [1, 3] .

The absolute minimum of the function is 11 in the interval [1, 3] .

The absolute maximum of the function is 11 in the interval [1, 3] .

The absolute minimum of the function is 15 in the interval [1, 3] .

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