设a＞0f(x)=ax2+bx+c曲线y=f(x)在点P(x0f(x0))处的切线的倾斜角的取值范围是［0］则P到曲线y=f(x)对称轴的距离的取值范围为…()A.［0］B.［0］C.［0||

Question

设a＞0 f(x)=ax ² +bx+c 曲线y=f(x)在点P(x ₀ f(x ₀ ))处的切线的倾斜角的取值范围是［0 ］ 则P到曲线y=f(x)对称轴的距离的取值范围为…(    )

A.［0 ］                      B.［0 ］

C.［0 | |                     D.［0 | |］

Answer 1

思路解析:f′(x 0 )=2ax 0 +b ∵倾斜角α的取值范围为0≤α≤ ∴0≤tanα≤1 即0≤2ax 0 +b≤1.∴ ≤x 0 ≤ .∴0≤x 0 + ≤ . ∴P到曲线y=f(x)对称轴的距离d=|x 0 + |∈［0 ］. 答案:B ...