IDZ Ryabushko Option 3 KR "Derivatives and their applic

Test "Derivatives and their applications" (2 hours). 260 pages

1. Find the first derivative of y′

2. Find the first derivative of y′
2.3 z = yarcsin((2y + 1)/3)

3. Calculate the first derivative of the function for the specified value of the argument or parameter or for the given coordinates of the point.
3.3 f(x) = xex/a, x = 0

4. Find the second derivative of y′′
4.3 y = x2lnx

5. Find the second derivative d2y/dx2 of the function.

6. Solve the following problems.
6.3. Determine the angle at which the curves x2 + y2 = 8 and y2 = 2x intersect?

7. Solve the following problems.
7.3. A body thrown upward moves according to the law s = −1/3t3 + 17/2t2 + 60t − 49 . At what moment in time will the speed of the body become equal to zero? Find the greatest height of the body´s ascent.