Question

高等数学第五题

Answer 1

lim(x->a) f'(x)/(x-a) =-1 (0/0)
=> f'(a) = 0
lim(x->a) f'(x)/(x-a) =-1 (0/0分子分母分别求导)
lim(x->a) f''(x) =-1
f''(a) =-1

追问

极大值极小值怎么判断

追答

f'(a) = 0
f''(a) =-1 <0 (max)
max f(x)= f(a) 极大值

追问

怎么证明呢

我能想出来，f'(x)是递减的

且f'(a)=0，所以f(a)是极大值

追答

如果还不明白，你应该看看书！
f'(a) = 0
f''(a) =-1 <0 (max)
max f(x)= f(a) 极大值

追问

追答

x=x0 (极大值极小值)

f'(x0) =0 and f''(x0) >0 极小值
f'(x0) =0 and f''(x0)<0 极大值