设a>0,f(x)=ax²+bx+c,曲线y=f(x)在点P(x0,f(x))处的切线的倾斜角的取值范围为[0,π/4,

题目

设a>0,f(x)=ax²+bx+c,曲线y=f(x)在点P(x0,f(x))处的切线的倾斜角的取值范围为[0,π/4,
则点P到曲线y=f(x)的对称轴距离的取值范围为
A、[0,1/a] B、[0,1/2a] C、[0,|b/2a|] D、[0,|b-1/2a|]

答案

(1)设:x=0,y=1 f(1/2)=f(x+y/2)=f(x)sin(a)+(1-sin(a))f(y) =f(0)sin(a)+(1-sin(a))f(1)=1-sin(a); 设:x=0,y=1/