Question

已知y=f(x)对一切的x满足(x^3)f''(x)+2x^2[f'(x)]^2+e^x=1.若f’'(x0)=0,x0

Answer 1

因为对一切的x满足x³f''(x)+2x²[f'(x)]²+e^x=1

令x=x0

因为f'(x0)=0

那么(x0)³f''(x0)+e^(x0)=1

f''(x0)=[1-e^(x0)]/(x0)³

因为x0≠0

所以,若x0>0,e^(x0)>1,(x0)³>0,那么f''(x0)