Question

设p为曲线C：y=x²+2x+3上在点，且曲线C在点P处切线倾斜角的的取值范围为[0.π/4]

则点P横坐标的取值范围为？

Answer 1

y'=2x+2
曲线C在点P处切线倾斜角θ的的取值范围为[0.π/4] tanθ∈[0,1]
倾斜角斜率k=tanθ=y'
0<=2x+2<=1
-2<=2x<=-1
-1<=x<=-1/2

Answer 2

y'=2x+2=tana
a∈[0.π/4]，0≤tana≤1
即
0≤2x+2≤1
-1≤x≤-1/2

Answer 3

-1<x<(π/4)-1