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.
3.24 ρ(φ) = φ/(1 – φ2), φ = 2

4. Find the second derivative of y′′
4.24 y = lntg(π/4 + x/2)

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

6. Solve the following problems.
6.24. In the equation of the parabola y = x2 + bx + c, determine b and c if it is known that the parabola is tangent to the line y = x at the point x = 2.

7. Solve the following problems.
7.24. The side of a square increases at a rate of 5 m/s. What is the rate of change of the perimeter and area of ​​the square at the moment when its side is equal to 50 m?

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