Calculus please help. Thank you.show work

1. A particle is moving according to the given data. Find the position of the particle. (5 pts.) a(t) = sint + 3cost s(0) = 0, v(0) - 2 2. Find the absolute min and absolute max of f (x) = 2x - 3x2/3 on the interval [-1,3]. (4pts.) 3. Verify the function f(x) = x + 2x + 4 satisfies the hypotheses of Mean Value Theorem on the interval [-1,0]. Then find all number c that satisfy the conclusion of the Mean Value Theorem. (4 pts.) 4. Analyze and sketch the graph of f(x) - 2(*-9) (17 pts.) a) Domain (1 pt.) b) Intercepts (2 pts.) c) Asymptotes (2 pts.) d) Symmetry (1 pts.) e) Increasing/Decreasing Interval (3 pts.) f) Local max/Local Min (1 pt.) g) Concave up/Concave down (3 pts.) h) Inflection point (1 pt.) i) Graph (3 pts.) 5. Which points on the graph of y - 4 - x2 are closest to the point (0,2)? (6 pts.)