IDZ Ryabushko Option 30 KR "Derivatives and their appli

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

1. Find the first derivative of y′

2. Find the first derivative of y′
2.30 y = tg2(x3 + 1)

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.
3.30 F(x) = 1/(x + 2) + 3/(x2 + 1), x = 0, x = 1

4. Find the second derivative of y′′
4.30 y = ln(x + √x)

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

6. Solve the following problems.
6.30. At what value of the parameter a does the parabola y = ax3 touch the curve y = ln x?

7. Solve the following problems.
7.30. A point moves in a straight line according to the law s = 60t – 5t3. After what period of time after the start of the motion will the point stop? Find the path traveled by the point during this time.