General Instructions: 1. Solve the following COMPLETELY, NEATLY, and ORDERLY. Write your answers on a piece of clean paper. 2. DO NOT CHEAT. Any form of cheating will be reprimanded. 3. Consult ONLY your instructor about this problem set. Do as indicated. 1, Using limit definition of derivative, determine whether f() = 5(t+5), 0 1 tiable at t = 1. (4 points) 2. Determine all points at which f(x) = 3 72 - 3 is differentiable. Justify your answer. (3 points) 3. FM Corporation is a company that manufactures face masks. For every a thousand pieces of face mask sold, the company's revenue (in thousand pesos) is R(x) = x(5 + x), x 2 0. a. If the company sold a thousand pieces of face mask, find the company's marginal revenue. Note: Marginal revenue is the increase in revenue that results from the sale of one additional unit of output. (2 points) b. Find the number of face mask sold if the company has a marginal revenue of Php 25,000. (2 points) 4. Find the second-order derivative of the following function: f(x) = log, cosa + In (6 points) 5. Let SA = 15/" + 10t + 20 and sp = 512 + 40t, t 2 0, be the position functions of cars A and B. respectively, that are moving along parallel straight lanes of a highway (here. z is in minutes and s is in feet). a. How far is car A ahead of car B when t = 0? (2 points) b. At what instant of time do they have the same velocity? Which car is ahead at this instant? (4 points) 6. In Genshin Impact, the optimal crit rate r to crit damage y ratio can be obtained by maximizing the product ry under the constraint a + , = c. Find the optimal crit rate and crit damage if c = 100% (6 points) 7. A 6-ft tall man is walking away from a 15-ft tall street lamp at the rate of 5 ft/sec. How fast is his shadow lengthening? (4 points)