Question

求问一道关于导数的题目

请问老师b选项为啥不对 谢谢🙏

Answer 1

e.g

f(x)
=x^4. sin(1/x) ; x≠0
=0 ; x=0
x=0 , f(x) 连续
f'(0)
=lim(h->0) [h^4. sin(1/h) -f(0)]/h
=0
x≠0
f'(x)
=4x^3. sin(1/x) + x^4. cos(1/x) . (-1/x^2)
=3x^2. sin(1/x) - x^2.cos(1/x)
f''(0)
=lim(h->0) [3h^2. sin(1/h) - h^2.cos(1/h) -f'(0) ]/h
=0
f(x) 只有一个“0”点