The function f (x) = x3-6x has a maximum and a minimum

f(x) = x^3 - 6x
F '(x) = 3 X2 - 6 = 0 x = soil √ 2
f''(x) = 6x
F '' (√ 2) = 6 √ 2 > 0 corresponds to the minimum value: F (√ 2) = 2 √ 2 - 6 √ 2 = - 4 √ 2
F '' (√ 2) = - 6 √ 2 < 0 corresponds to the maximum value: F (- √ 2) = - 2 √ 2 + 6 √ 2 = 4 √ 2

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