Directions: Answer all questions. You must show your handwritten work for all of these and clearly identify your answer. NO TYPED WORK!!! You may print this assignment out and work directly on it or copy the problems and work on separate paper. When you are done you must upload it and send it to me as an attachment. Please use Blackboard h -0 1. Use the definition of derivative lim (@)-1 to find the slope of the tangent of y = x2 at x = -3 (4 points) 2. Find the equation of the tangent line to y = x2+3 2x - at (1,2). (4 points)3. Given the function y = x4 + 2x3, determine (6 points) 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) = t3 - 11t2 + 24t where s(t) is (8 points) 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 direction5. The concentration "C" of a certain chemical in the bloodstream "t" hours after [6 points) 3: ' When, to the nearest 2? H3 hundredth of an hour, is the concentration the greatest? injection into muscle tissue is given by C = 6. A company has started selling a new type of smartphone at the price of 110 0.051: 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 05:01: and cost is given by C(x) = 50:: + 6000. How many smartphones should the company manufacture per dag,r to maximize prot? (6 points) 7. A company has determined the demand curve for their product is D = 'f 5000 - p2, where p is price in dollars and D is quantity in millions. If weather conditions are driving the price up $2 a week, nd 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)