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

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.
3.26 s(t) = 3/(5 – t) + t2/5, t = 0, t = 2

4. Find the second derivative of y′′
4.26 y = x/(x2 – 1)

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

6. Solve the following problems.
6.26. Find the angle at which the parabolas y = (х – 2)2 and y = –4 + 6х – х2 intersect.

7. Solve the following problems.
7.26. The distance s m traveled by a body in t s is determined by the formula 65s = t3/8 + 3t2 + t. Find the speed and acceleration of the body at t = 10.

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