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.
3.2 f(x) = √x + 2√x, x = 1

4. Find the second derivative of y′′
4.2 y = arctan(x2)

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

6. Solve the following problems.
6.2. Show that the hyperbolas xy = 8 and x2 – y2 = 12 intersect at right angles?

7. Solve the following problems.
7.2. Two points move in a straight line according to the laws s1 = t3 – 3t and s2 = t3 – 5t2 + 17t – 4. At what point in time will their velocities be equal?

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