Full Mock Exam Matematica

Mock Final Exam - 2025-26 EPOS 29-12-2025 n. 1

Write the number of the correct answer in the corresponding box

Answers STUDENT NAME AND ID NUMBER :

Question 1 2 3 4 5 6 7 8

Question 1) [3 points] Let f be a twice differentiable, increa- Question 5) [3 points] Calculate the definite integral

sing and convex function in the interval (a, b). Select the correct 3

Z 1

statement: ( + 7x)dx

2

x

2

√

′ ′′ ≥ ∈

1) f (x) + 2f (x) 0 for all x (a, b) and select the correct statement:

2) None of the other statements is correct

3) There exist a local maximum in (a, b) 1) None of the other statements is correct

′ ′′

≥ ∈

4) f (x) f (x) for all x (a, b) 2) The value of the integral is 1

53

3) The value of the integral is

Question 2) [3 points] Given the function f (x) = ln (x + 1) + 3

√ 55

4) The value of the integral is

2x + 4, select the correct statement: 3

Question 6) [3 points] Given the function of two variables,

′′ 1 1

−

1) f (x) = +

2 2 2

1/2

(x+1) − −

(2x+4) f (x, y) = x y 2xy + 3x + 3, select the correct statement:

2) None of the other statements is correct.

3) The second order Taylor polynomial in x = 0 is 34 34

0 1) , is a saddle point

2

3 98

−

y = 2 + x x 2) None of the other statements is correct

2

4) The second order Taylor polynomial in x = 0 is 34

34

0 − , is a saddle point

3)

2

3 9

−

y = 2 + x x 34 34

−

4) , is a local minimum point

2 16

Question 3) [3 points] Given the function of two variables x 3

Question 7) [3 points] Given the function f (x) = e x ,

−

f (x, y) = 2xy + 2y 3 under the constraint x + 3y = 4. Select ′′

calculate f (x) and select the correct statement:

the correct statement: 1) f is concave in R √

3 56

1) is a constrained local minimum point

, − 3, 0)

2) f is convex in [−3

2 √

2) A critical point of the associated Lagrangian function is 3) f is concave in [−3 + 3, +∞)

5 5

3

, , 4) none of the other statements is correct

2 3 6

3) None of the other statements is correct

4) A critical point of the associated Lagrangian function is +∞ −n+1

P ·

Question 8) [2 points] Given the series 3 (−2) ,

n=2

3 5 5

, , select the correct statement:

2 6 3

Question 4) [3 points] Given the function in two variables 1) None of the other statements is correct

7x+1 , select the correct statement:

f (x, y) = e y−3 −1.

2) Its value is −3.

3) Its value is

1) None of the other statements is correct 4) Its value is 1.

7x+1

∂f 1

− e

2) (x, y) = y−3

2

∂y (y−3)

7x+1

∂f 7

3) (x, y) = e y−3

∂x y−3

7x+1

∂f

4) (x, y) = 7e y−3

∂x