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.
3.27 y = e√lnx, x = e

4. Find the second derivative of y′′
4.27 y = x – arctgx

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

6. Solve the following problems.
6.27. Find the angles at which the ellipse x2/4 + y2 = 1 and the parabola 4у = 4 – 5х2 intersect.

7. Solve the following problems.
7.27. A rotating flywheel, held by a brake, rotates in t s by an angle φ = a + bt – ct2, where a, b, c are positive constants. Determine the angular velocity and acceleration of rotation of the wheel. When will the wheel stop?

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