f(x)在(-∞,3]上是否有拐点?
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发布时间：2024-10-24 13:24
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热心网友
时间：2024-11-09 07:50
f'(x) =6x^2-12x-18
f'(x)=0
6x^2-12x-18=0
x^2-2x-3=0
(x-3)(x+1)=0
x=3 or -1
f''(x) = 12x-12
f''(3) =36-12=24>0 (min)
f''(-1) =-12-12=-24<0 (max)
min f(x) = f(3)=2(3)^3-6(3)^2-18(3)-7 =-61
max f(x) = f(-1) =2(-1)^3-6(-1)^2-18(-1)-7 =3
f''(x) >0
12x-12 >0
x>1
凹区间为 (1,+无穷)；凸区间为 (-无穷, 1)
没有拐点
