National Math exam 2024

Question 1 (2 points)

Find the derivative of f(x) = x^3 · sin(x) and evaluate at x = 0.

Question 2 (3 points)

A particle moves along a line with velocity v(t) = 4t - 3. Find the displacement between t = 1 and t = 3.

Question 3 (5 points)

State and prove the Mean Value Theorem, then give a geometric interpretation.