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Q: (c) F{-h(x+ 1) + 2h(x) – h(x – 1)}, where h(x) is the unit step function defined on page 235 of the…
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- If xis large, which function grows faster, f(x)=2x or g(x)=x2?Suppose for a company the function of income (in dollars) is given by R(x)=-0.12x^3+1,296x+12201 where x is represented by the number of unities sold. Then the maximum income is: Choose the correct answerA company operates a fleet of delivery trucks. Study shows that gallons of fuel consumed per mile of driving, F(x), is related to the speed at which a truck is driven, x miles per hour, by the function: F(x) = k1/x +k2x; 10≤ x≤ 80, where k1 and k2 are parameters that vary somewhat from truck to truck. Now, Find and write the expression for the speed, x, that will lead o minimal fuel consumption per mile driving. What speed will provide minimal fuel consumption per mile of driving for a truck having k1 = 4.9, k2 = 0.004?
- The revenue from the sale of x mineral-based makeup sets is given by R(x)=42x−0.4x^2 dollars. The total cost is given by C(x)=0.1x^2−30x+2430 dollars, where 0≤x≤110. Determine the interval of sales for which the profit is increasing and the interval for which it is decreasing. Express your answer in open intervals.A manufacturer finds that the revenue generated by selling x units of a certain commodity is given by the function R(x) = 80x − 0.4x2, where the revenue R(x) is measured in dollars. What is the maximum revenue, and how many units should be manufactured to obtain this maximum? $_____________, at___________ unitsFind the maximum and minimum values of the function y=4x^(3)−4x+6 on the interval [0,2]. (Use decimal notation. Give your answer to three decimal places.)
- Suppose the function of earnings (in dollars) is given by G(x)=10x^3-320x^2+3410x-12090 where x is the quantity of product that is produced and sold. Suppose that this function is defined in the intervals [9, 12] G has a relative minimum if x equals______ G has a relative maximum if x equals______ The absolute maximum of the function of earnings G(x) occurs if x is equal to_____ Tha maximum earning in this case is equal to $______dollarsFind the slope m of the line tangent to the graph of the function f(x) = 5 - 6x at point (-1, 11)With a function of x^4 - 50x^2 + 9, and increasing intervals at [-5, 0] and [5, infinity), and decreasing at (-infinity, -5] and [0, 5], what are the two inflection points?
- In a board game, a certain number of points is awarded to a player upon rolling a six sided die (labeled 1 to 6) according to the function f(x) = 2x - 1, where a is the value rolled on the die. Find and interpret the given function values and determine an appropriate domain for the function. f(1) = ___， meaning when a __is rolled on the die, the player is awarded ___points. This interpretation ___ (makes sense/does NOT make sense) the context of the problem. f(5.5) = --- meaning when a ___is rolled on the die, the player is awarded --points. This (makes sense/does NOT make interpretation sense) in the context of the problem. f(7) =---, meaning when a ___is rolled on the die, the player is awarded___points. This interpretation ___（makes sense/does NOT make sense) in the context of the problem. Based on the observations above, it is clear that an appropriate domain for the function is__- (all real numbers /non-negative real numbers /real numbers in a≤x≤b /integers /whole numbers 0,…A manufacturer finds that the revenue generated by selling x units of a certain commodity is given by the function R(x) = 100x − 0.4x2, where the revenue R(x) is measured in dollars. What is the maximum revenue, and how many units should be manufactured to obtain this maximum?A closed right circular cylinder will be built with two types of metal. The base and the top of the cylinder will be constructed of metal that has a value of $ 2 per cm2, while The side surface of the cylinder will be constructed of a metal that costs $ 2.5 per cm2. The function that allows to minimize the cost of manufacturing said cylinder is given by: the answers are in the first attached image