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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![1. Suppose C(x) is a function representing the cost (in dollars) of producing x units
of energy, and R(x) is a function representing the revenue (in dollars) of selling x
units of energy. Suppose further that both functions are continuous for all x > = 0.
A. Is there necessarily some x value, let's call it C, that will maximize profit over
all x > = 0? Explain your answer.
%3D
B. Suppose we know we can't produce more than 1,000 units of energy. Is
there necessarily some x-value, call it C, that will maximize profit over the
interval [0,1000]? Explain your answer.
C. Again, assume that we can't produce more than 1,000 units of energy. Is
there necessarily some x value, let's call it C, for which the profit is exactly 0?
Explain your answer.
2. Produce a function f(x) that satisfies the following conditions:
A. I. Its domain is all real numbers. II. It has no maximum and no minimum on
the interval [ 1,3] . III. It satisfies f(1) = 1 and f(3) = -1, but there does not exist
ac between 1 and 3 such that f(x) = 0.
%3D
B. I. f is continuous for all x. II. -10< = f(x) < = 10 for all x. II.f does not have a
maximum or minimum on the interval [negative infinity, infinity].
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa2e50573-b000-490e-892a-bd3af2ad7850%2Fafd8e444-b35f-479f-a4a2-20e4532dff6a%2Fj4a36xo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Suppose C(x) is a function representing the cost (in dollars) of producing x units
of energy, and R(x) is a function representing the revenue (in dollars) of selling x
units of energy. Suppose further that both functions are continuous for all x > = 0.
A. Is there necessarily some x value, let's call it C, that will maximize profit over
all x > = 0? Explain your answer.
%3D
B. Suppose we know we can't produce more than 1,000 units of energy. Is
there necessarily some x-value, call it C, that will maximize profit over the
interval [0,1000]? Explain your answer.
C. Again, assume that we can't produce more than 1,000 units of energy. Is
there necessarily some x value, let's call it C, for which the profit is exactly 0?
Explain your answer.
2. Produce a function f(x) that satisfies the following conditions:
A. I. Its domain is all real numbers. II. It has no maximum and no minimum on
the interval [ 1,3] . III. It satisfies f(1) = 1 and f(3) = -1, but there does not exist
ac between 1 and 3 such that f(x) = 0.
%3D
B. I. f is continuous for all x. II. -10< = f(x) < = 10 for all x. II.f does not have a
maximum or minimum on the interval [negative infinity, infinity].
%3D
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