What is the maximum value of the function f(x) = 2x^3 - 2x - 6 in the interval [0, 2]? A. -6 B. 6 C. 10 D. 5.5

GATE 1997 · Engineering Mathematics · Maxima Minima · medium

Answer: B. 6

1. Find critical points: f'(x) = 6x^2 - 2 = 0 => x^2 = 1/3 => x = sqrt(1/3) approx 0.577 (taking positive root in [0,2]).
2. Evaluate at critical point and endpoints: f(0) = 0 - 0 - 6 = -6. f(sqrt(1/3)) = 2*(1/3)^(3/2) - 2*(1/3)^(1/2) - 6 approx 0.385 - 1.155 - 6 = -6.77. f(2) = 2(8) - 2(2) - 6 = 16 - 4 - 6 = 6.