1. (5 pts) Find a formula for a cubic polynomial y = f(x) in factored form, whose graph matches the one shown below. Then expand your polynomial (multiply it out into standard form). 2 ( -1, 0) (2, 0) (3, 0) -2 0 -2 (0, -3)(2 pts) Does the following limit exist? If 50, show work to find the value. If not, explain why not. 3123}; 1'06) (1pt) Find lim f(x) x>1 (1pt) Find lim f(x) x>1+ (1 pt) Based on your results above, does lim f(x) exist? If so, find the value. If not, explain x)_1 why not. 3. (11 pts total] The height in meters of a tomato thrown up in the air is Mt) = 4.91.'2 + 78.41: + 3, where t is the number of seconds since the tomato was thrown. a. (3 pts] Find the average velocity of the tomato between t = 2 and t = 5 seconds. Include units in vourfinal answer. b. (5 pts] Use the limit definition of the derivative to verify that the (instantaneOus) velocity is v 2 EU) 2 9.8t + 78.4. c. (3 pts) If the tomato's velocity is D at the time it reaches its maximum height, use the equations for Mt) and h'[t) given above to determine the tomato's maximum height. Include units in your answer. 4. (6 pts total) Let P(t) represent the population of Metropolis in millions of people, where t is the number of years since 1970. Interpret the meaning of the following statements in everyday terms {that a person not ta king Calculus would understand). Be sure to include units in your explanations. a. (1 pts) P[5) = 6.4 (6 pts total) Let PU) represent the population of Metropolis in millions of people, where t is the number of years since 1970. Interpret the meaning of the following statements in everyday terms (that a person not taking Calculus would understand). Be sure to include units in your explanations. a. (1 pts) P[5) = 6.4 b. (2pts) P'(5)=D.7 c. (3 pts) Use the values in parts a and b above to approximate the population of Metropolis in 1980. 5. a. (3 pts) Find the value(s) of x for which the piecewise function f(x) graphed below appears to not be differentiable. For each value, briefly explain why the function is not differentiable at that point. 5 (3, 5) -5 0 5b. (3 points) Using the graph above, write the following four values in order, from smallest to largest: (Careful! Note that the first three values involve f'whlle the last value, f(2), does not involve the derlvatlve.) f '(-5) f '(0) f '(2) f (-2)