Nilai minimun f(x)=x³+3x²-24x-46

jawab

f(x) = x³  + 3x² - 24x - 46
f'(x) = 0
3x² + 6x - 24 =0
x² + 2x - 8 =0
(x +4)(x - 2) = 0
x = -4 atau x =  2

f "(x) = 6x + 6
f"(-4) = 6(-4) + 16 = -18 → f''(-4) < 0 → maksimum
f"(2) = 6(2) + 6 = 18 → f" (2) > 0 → minimum
x = 2,  f(2) = (2³) + 3 .2² - 24(2) - 46 = - 74
nilai minimum = - 74