Question

設(shè)a>0,f(x)=ax2+bx+c,曲線y=f(x)在點(diǎn)P(x0,f(x0))處切線的傾斜角的取值范圍為[0,],則點(diǎn)P到曲線y=f(x)的對(duì)稱軸的距離的取值范圍為　　　　.

 

Answer 1

[0,]

【解析】∵y=f(x)在點(diǎn)P(x0,f(x0))處切線的傾斜角的取值范圍為[0,],∴0≤f'(x0)≤1,即0≤2ax0+b≤1.又∵a>0,

∴-≤x0≤,∴0≤x0+≤,即點(diǎn)P到曲線y=f(x)的對(duì)稱軸的距離的取值范圍為[0,].