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1. [S. points] The revenue (in dollars) from the sale of x collectible dolls is given by the function R(x) = 46x - 0.02x3 for 0 S x 5 3200 a. Find the average change in revenue if the production is changed from 1,400 dolls to 1,800 dolls. b. Use the 4-Step Process described in Module 4 to find the instantaneous rate of change of revenue when 1,400 dolls are produced. c. Interpret and compare your results for parts a. and b. Use the context and units of the problem in your interpretation. 2. Use the basic rules of derivatives for each of the following. a. Find f'(x) for the function: 1 ( x ) = 5+ 5x1 - 3Vx+ 12 b. Find for the function: x + 2x - 1 xx5+3x2 3. For the function g(x) = (x2+ 3) (x - x2 + 19): a. Use the Product Rule to find g'(x). b. Rewrite the function g (x) as a polynomial by multiplying (x? + 3x) and (x4 - x2 + 19). c. Use the basic derivative rules to find g'(x) using the version of g (x) you found in part d. Verify that the g'(x) that you found in part a. is equal to the g'(x) that you found in part 4. [5 points] The price p (in dollars) and the demand for x industrial fans are related by the equation p = 50 (5000 -x). a. Find the revenue function, R(x). b. Find the R'(x). c. What is the rate of change of the revenue when 2,300 fans are produced. Interpret your results using the context and units of the situation in the problem. 5. A pop-star (named Pop Star) is pregnant and expects to have her baby in 2022. When the baby is 18 years old, Pop Star plans to send the child (named Child) to Private College The Private College is pretty expensive right now. They say that, 18 years from now, it will cost $784,000 to pay four years of tuition for Child. Pop Star's business manager has found an off shore account that will pay 3.4% interest compounded continuously. How much does Pop Star need to invest today, so that she will have the correct amount for Child to pay four Years tution? Round your answer to the nearest whole dollar