Question

f(x)＝g(x)/x,x≠0；0,x＝0,其中g(x)可导,且在x＝0处二阶导数g''(0)=3,且g(0)＝g'(0

Answer 1

f '(0)=lim[x→0] [f(x)-f(0)]/x

=lim[x→0] [g(x)/x-0]/x

=lim[x→0] g(x)/x²

洛必达法则

=lim[x→0] g'(x)/(2x)

=(1/2)lim[x→0] [g'(x)-g'(0)]/x

=(1/2)g''(0)

=3/2

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