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Question 6: For each of the following functions f, find its natural domain. (a) f(x) = 22-2-3 (b) f(x)=√x+7-√√x² + 2x − 15 - (c) f(x) = 2¹-5

Question 6: For each of the following functions f, find its natural domain. (a) f(x) = 22-2-3 (b) f(x)=√x+7-√√x² + 2x − 15 - (c) f(x) = 2¹-5

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question 6: For each of the following functions f, find its natural domain. (a) f(x) = 7²-2x-3 (b) f(x)=√x+7-√√x² + 2x − 15 (c) f(x) = 25 Question 8: A company manufactures and sells x pieces of certain product per month. The monthly cost in (dollars) is C'(x) = 120000 + 100x and the price-demand equation is x 15 where 0≤x≤ 4000. Find the production level that will give the maximum profit, and the maxi- mum profit. p(x) = 300 - Question 9: The market research department of company recommends that the company man- ufacture and market a new transistor radio. The cost C(r) and price-demand p(x) functions are given below: C(x)= 7000 + 2x² p(x) = 100.001x where is the number of radios retailers are likely to buy $p per radio (a) Find the domain of the function defined by the price-demand equation (2). (b) Find the marginal cost and marginal average cost at x = 2000 and interpret the results. (c) Find the marginal revenue and marginal average revenue at x = 2000. (d) Find the profit function and its domain, and marginal profit at x = 1000 and interpret the result. (1) (2) Question 10: For each of the following function f defined by : f(x) 2³ + 3x² 45, and f(x) = 27x-x³ (a) Find all critical points of function f. (b) Find the maximum and minimum points of function f. (c) Determine the intervals where the function f is increasing, where it is decreasing. Question 11: Evaluate the following: [₁2³ (9-7x4¹) da
Transcribed Image Text:Question 6: For each of the following functions f, find its natural domain. (a) f(x) = 7²-2x-3 (b) f(x)=√x+7-√√x² + 2x − 15 (c) f(x) = 25 Question 8: A company manufactures and sells x pieces of certain product per month. The monthly cost in (dollars) is C'(x) = 120000 + 100x and the price-demand equation is x 15 where 0≤x≤ 4000. Find the production level that will give the maximum profit, and the maxi- mum profit. p(x) = 300 - Question 9: The market research department of company recommends that the company man- ufacture and market a new transistor radio. The cost C(r) and price-demand p(x) functions are given below: C(x)= 7000 + 2x² p(x) = 100.001x where is the number of radios retailers are likely to buy $p per radio (a) Find the domain of the function defined by the price-demand equation (2). (b) Find the marginal cost and marginal average cost at x = 2000 and interpret the results. (c) Find the marginal revenue and marginal average revenue at x = 2000. (d) Find the profit function and its domain, and marginal profit at x = 1000 and interpret the result. (1) (2) Question 10: For each of the following function f defined by : f(x) 2³ + 3x² 45, and f(x) = 27x-x³ (a) Find all critical points of function f. (b) Find the maximum and minimum points of function f. (c) Determine the intervals where the function f is increasing, where it is decreasing. Question 11: Evaluate the following: [₁2³ (9-7x4¹) da
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