1. Use the definition of derivative lim of y = x at x = -3 f(x+h)-f(x) to find the slope of the tangent h0 h (4 points) 2. Find the equation of the tangent line to y = x+3 2x at (1,2). (4 points) 3. Given the function y = x + 2x, determine a.) the intervals where the function is concave up b.) the intervals where the function is concave down c.) the coordinates of the inflection points 4. Given the position of a particle s(t) = t - 11t + 24t where s(t) is measured in meters and t is time in seconds determine: a. position at 3 seconds b. velocity at 3 seconds c. acceleration at 3 seconds d. the interval(s) where the particle moves forward e. the interval(s) where the particle moves backward f. at what time "t" the particle changes direction (6 points) (8 points) 5. The concentration "C" of a certain chemical in the bloodstream "t" hours after injection into muscle tissue is given by C = When, to the nearest hundredth of an hour, is the concentration the greatest? 3t 27+t3 (6 points) 6. A company has started selling a new type of smartphone at the price of 110-0.05x where x is the number of smartphones manufactured per day. The parts for each smartphone cost $50 and the labor and overhead for running the plant cost $6,000 per day. If the revenue is given by R(x) (110 - .05x)x and cost is given by C(x) = 50x + 6000. How many smartphones should the company manufacture per day to maximize profit? (6 points) 7. A company has determined the demand curve for their product is D = 5000-p, where p is price in dollars and D is quantity in millions. If weather conditions are driving the price up $2 a week, find the rate, to the nearest hundredth, at which demand is changing when the price is $40. Make sure to answer the question using a sentence. (6 points)