Question

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

A.［0,］                      B.［0,］

C.［0,||                     D.［0,||］

Answer 1

思路解析:f′(x₀)=2ax₀+b,∵傾斜角α的取值范圍為0≤α≤,

∴0≤tanα≤1,即0≤2ax₀+b≤1.∴≤x₀≤.∴0≤x₀+≤.

∴P到曲線y=f(x)對(duì)稱軸的距離d=|x₀+|∈［0,］.

答案:B