If x is a real number, the function f(x) = x^3 + x^2 + x + 1 has: - Mathematics MCQ Mathematics Mock Test - 3 2026 | ExamTest.live

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If x is a real number, the function f (x) = x^{3} + x^{2} + x + 1 has:

Solution & Step-by-step Explanation

f^{'} (x) = 3 x^{2} + 2 x + 1 To find critical points, set f^{'} (x) = 0 : 3 x^{2} + 2 x + 1 = 0 Discriminant D = b^{2} - 4 a c = 2^{2} - 4 (3) (1) = 4 - 12 = - 8 Since D < 0, f^{'} (x) has no real roots.Because there are no critical points where the derivative changes sign, the function is strictly increasing and has no local maxima or minima.

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If x is a real number, the function f (x) = x^{3} + x^{2} + x + 1 has:

maximum value at x = 0

minimum value at x = 1

maximum value at x = - 1

neither maximum nor minimum value

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