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!