IDZ 6.4 - Option 16. Decisions Ryabushko AP

1. Solve the following tasks:
1.16 lamp hanging over the center of a round table of radius r. At what height above the table lamp lighting object lying on its edge, will be the best? (Lighting is directly proportional to the cosine of the angle of incidence of light rays, and inversely proportional to the square of the distance from the light source.)

2. Carry out a full investigation of these functions and build their schedules.
2.16 y = ln (x2 + 1)

3. Carry out a full investigation of these functions and build their schedules.
3.16 y = x3 / (9 - x3)

4. Find the minimum and maximum values of the function y = f (x) on the interval [a; b]
4.16 y = e4x - x2, [1; 3]