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

1. Find the first derivative of y′

2. Find the first derivative of y′

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.
3.29 f(x) = (x2 + x + 1)(x2 – x + 1), x = 0, x = 1

4. Find the second derivative of y′′
4.29 y = arctan√x

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

6. Solve the following problems.
6.29. Find the tangent to the curve 4x2 + y2 = 80, parallel to the line x + y – 6 = 0.

7. Solve the following problems.
7.29. During the acceleration period, the flywheel rotates according to the law φ = t3/10. After what time after the start of the movement will the angular velocity of the flywheel be equal to 60π rad/s? What will be the angular acceleration of the body at this moment?

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