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

1. Find the first derivative of y′

2. Find the first derivative of y′
2.1 y = 3arctg2(4x + 1)

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.
3.1 f(x) = (1 – 2x)/(1 + 3√2x), x = 4

4. Find the second derivative of y′′

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

6. Solve the following problems.
6.1. At what angle does the sinusoid y = sinx intersect the line y = 1/2?

7. Solve the following problems.
7.1. The law of motion of a material point along a straight line is given by the formula s = t3 – 3t2 + 3t + 5. At what moments of time t is the speed of the point equal to zero?

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