Calculus please help. Thank you.show work

Math 260- Test 3 Total:36 pts. 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, (0) =2 2. Find the absolute min and absolute max of f (x) = 2x - 3x7/3 on the interval [-1,3]. (4pts.) 3. Verify the function f(x) = x8 + 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.)