The function f(x) = x^3 - 3 x has: - Mathematics MCQ Mathematics Mock Test - 5 2026 | ExamTest.live

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The function f (x) = x^{3} - 3 lo g x has:

Solution & Step-by-step Explanation

1. Find f^{'} (x) : f^{'} (x) = 3 x^{2} - \frac{3}{x} 2. Set f^{'} (x) = 0 for critical points: 3 x^{2} = \frac{3}{x} ⟹ x^{3} = 1 ⟹ x = 1 3. Find f^{''} (x) : f^{''} (x) = 6 x + \frac{3}{x ^{2}} 4. Test at x = 1 : f^{''} (1) = 6 (1) + \frac{3}{1 ^{2}} = 9 Since f^{''} (1) > 0, x = 1 is a point of local minima.

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The function f (x) = x^{3} - 3 lo g x has:

local maxima at x = 1

local minima at x = 3

local maxima at x = 0

local minima at x = 1

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