IDZ 6.4 - Option 12. Decisions Ryabushko AP

1. Solve the following tasks:
1.12 of round logs with a diameter d have to cut the rectangular beam. What should be the width and height h b of this section to the beam being horizontally disposed and uniformly loaded, had the smallest deflection? (The amount of deflection is inversely proportional to the product of the width b of the cross-sectional area and the height of the cube h)

2. Carry out a full investigation of these functions and build their schedules.
2.12 y = x3e-x2 / 2

3. Carry out a full investigation of these functions and build their schedules.
3.12 y = x2 / (x + 2) 2

4. Find the minimum and maximum values of the function y = f (x) on the interval [a; b]
4.12 y = (x - 2) ex, [-2; 1]