y & lt=-x+4
Make up the area under OA and AB.
Because y & gt=kx
∴k<; = 1
∫ OA ⊥ AB (1* (1) =-1,vertical)
∴△ Height OA of ∴△OAB = 2 √ 2 (distance from point to straight line)
1/2 * 2√2 * AB & gt; =2
∴ab>; =√2
Minimum AB=√2
At this time, b is (3, 1).
∴k has the maximum value = 1/3.
choose one
If you agree with my answer, please click "adopt as satisfactory answer" and wish you progress in your study!