C

2010012502

Level: 
C
Identify a true statement about the function f(x)=x3+6x2+12x−1.
There is neither local minimum nor maximum of f.
The function f has a local maximum at the point x=−2.
The function f has a local minimum at the point x=−2.
The global minimum of f on R is at x=−2.

2010012501

Level: 
C
Find the global extrema of the following function on the interval [0;2]. f(x)=x3+3x2−9x
the global minimum at x=1, the global maximum at x=2
the global minimum at x=1, the global maximum at x=−3
the global minimum at x=2, the global maximum at x=1
the global minimum at x=0, the global maximum at x=2

2010008707

Level: 
C
Let ABCDEFGH be a cube with an edge length of 2 units placed in the rectangular coordinate system. In the cube a regular tetrahedron BDEG is highlighted (see the picture). Find the angle between its faces and round the number to the nearest minute.
70∘32′
45∘0′
51∘4′
54∘44′

2010008706

Level: 
C
A cube ABCDEFGH with an edge length of 4 units is placed in a coordinate system (see the picture). Find an angle ψ between the plane ρ passing through the points B, D and H and the straight line CF. Hint: An angle between a line and a plane is an angle between the line and its orthogonal projection into this plane.
ψ=π6
ψ=π12
ψ=π4
ψ=π3