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- Suppose that average annual income (in dollars) forthe years 1990 through 1999 is given by the linearfunction: I(x)=1,054x+23,286 , where x is thenumber of years after 1990. Which of the followinginterprets the slope in the context of the problem? a. As of 1990, average annual income was $23,286. b. In the ten-year period from 1990-1999, averageannual income increased by a total of $1,054. c. Each year in the decade of the 1990s, averageannual income increased by $1,054. d. Average annual income rose to a level of $23,286 bythe end of 1999.Polynomial Function of Data y = 1.2889x3 - 358.53x2 + 48536x - 34188 What is the second derivative, what is the point of inflection and round x to the nearest whole number its corresponding date? Explain the implications of the point of inflectionRevenue If the price from the sale of x units of aproduct is given by the function p = 100x - x2,the revenue function for this product is given byR = px = (100x - x2)x.a. Find the numbers of units that must be sold to givezero revenue.b. Does the graph of the revenue function verify thissolution?
- Find the slope of the curve y^2 = 3x + 1 at the point (−1/3, 0). Draw the graph of the curve. (solve by definition/long method)Application of Differential Calculus: Optimization Farmers use a certain plant food costing $4.00 per ounce to help them in growing oranges. It is estimated that when x ounces of the food are used on an ace of orange grove, the farmer is able to get Ln(4x+5) crates of oranges from that acre of land. If the farmer can sell the oranges at $20 per crate, how many ounces should be used per acre to maximize the orange crops net value.(a) Find a polynomial function of degree 3 whose y-interceptis 5 and whose x-intercepts are - 2, 3, and 5. Graph thefunction.(b) Find a rational function whose y-intercept is 5 and whosex-intercepts are - 2, 3, and 5 that has the line x = 2 as avertical asymptote. Graph the function.
- a polynomial function is given P(x)= x(x^2-4) describe the end behavior of the polynomial function. end behavior: y-->_____ as x--> inifnity y-->______ as x--> - inifinityThe profit function of Acrosonic company is given by P(x)=-0.02x^2+300x-200,000 dollars, where x is the number of Acrosonic model F loudspeaker systems produced. Find where the function P is increasing and decreasing. 1.) Increasing a.) The profit function P is increasing on(7500,∞) b.) The profit function P is increasing on(7500,0) c.) The profit function P is increasing on (0,7500) d.) The profit function P is increasing on(∞,7500) 2.) Decreasing a.) The profit function P is decreasing on(7500,∞) b.) The profit function P is decreasing on(7500,0) c.) The profit function P is deccreasing on (0,7500) d.) The profit function P is decreasing on(∞,7500)Find the maximum profit and the number of units that must be produced and sold in order to yield the maximum profit. Assume that revenue, R(x), and cost, C(x), of producing x units are in dollars. R(x)=50x−0.1x2, C(x)=4x+15 In order to yield the maximum profit of $ , units must be produced and sold.
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