Hello !
f(x) = 2x³ - 3x² - 12x + 3
f'(x) = 6x² - 6x = 6x(x - 1)
f''(x) = 12x - 6
The function is concave up for f''(x)＞0 ==> 12x - 6＞0 ==> x＞1/2
Thus the smallest number is 1/2
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Verified answer
Hello !
f(x) = 2x³ - 3x² - 12x + 3
f'(x) = 6x² - 6x = 6x(x - 1)
f''(x) = 12x - 6
The function is concave up for f''(x)＞0 ==> 12x - 6＞0 ==> x＞1/2
Thus the smallest number is 1/2