You are encouraged to work on this assignment collaboratively with your peers in class. You can also ask me for hints if you are stuck. Yet you should write up your own work and submit it on Canvas in ONE pdf file. Show all of your work for full credit, and your work should be clearly written and organized. Problem 1. Calculate F'(0), where F(x) = 3x + 5x + 5x +1 8x9 - 7x4 + 1 Hint 1: Do not calculate F(x) directly. Instead, write F(x) _ J (x) and express F' (0) g(x) directly in terms of f (0), f'(0), g(0), and g'(0). Hint 2: I asked a similar question in the midterm last quarter and the solution is some- where on Canvas...Problem 3. Calculate the first three derivatives of the function f (x) =x-2. Then find a general formula for f(") (x). Hint: Try NOT multiplying the coefficients together and observe any pattern you see.Problem 2. Suppose a stone is thrown vertically upward with an initial velocity of 64 ft/sec from a bridge 96 ft above a rive. (a) Find the position function s(t) and the velocity function v(t). (b) What is the highest point above the river reached by the stone? (c) With what velocity will the stone strike the river?Problem 4. Find an equation of the tangent line of the following function f(x) = 2 (sin r - cos r) at the point where r =