Answer the following questions for the function defined on the interval [-6.18, 0.57]. Remember that you can enter pi for π as part of your answer. -3-л a.) f(x) is concave down on the region(s) 2 2 f(x) = = sin² (-1/2) b.) A global minimum for this function occurs at (-π,1)) c.) A local maximum for this function which is not a global maximum occurs at ((0.57,0.079) d.) The function is increasing on the region(s) (-6.18, -π) U (0, 0.57) Note: In some cases, you may need to give a comma-separated list of intervals, and intervals should be given in interval notation. Using Interval Notation ■ If an endpoint is included, then use [ or ]. If not, then use ( or ). For example, the interval from -3 to 7 that includes 7 but not -3 is expressed (-3,7]. ■ For infinite intervals, use Inf for ∞ (infinity) and -Inf for - (-Infinity). For example, the infinite interval containing all points greater than or equal to 6 is expressed [6, Inf). ■ If the set includes more than one interval, they are joined using the union symbol U. For example, the set consisting of all points in (-3,7] together with all points in [-8,-5) is expressed [-8,-5) U(-3,7]. ■ If the answer is the empty set, you can specify that by using braces with nothing inside: { } ■ You can use R as a shorthand for all real numbers. So, it is equivalent to entering (-Inf, Inf). ■ You can use set difference notation. So, for all real numbers except 3, you can use R-{3} or (-Inf, 3) U(3, Inf) (they are the same). Similarly, [1,10)-{3,4} is the same as [1,3)U(3,4)U(4,10). ■ WeBWorK will not interpret [2,4] U[3,5] as equivalent to [2,5], unless a problem tells you otherwise. All sets should be expressed in their simplest interval notation form, with no overlapping intervals.
Answer the following questions for the function defined on the interval [-6.18, 0.57]. Remember that you can enter pi for π as part of your answer. -3-л a.) f(x) is concave down on the region(s) 2 2 f(x) = = sin² (-1/2) b.) A global minimum for this function occurs at (-π,1)) c.) A local maximum for this function which is not a global maximum occurs at ((0.57,0.079) d.) The function is increasing on the region(s) (-6.18, -π) U (0, 0.57) Note: In some cases, you may need to give a comma-separated list of intervals, and intervals should be given in interval notation. Using Interval Notation ■ If an endpoint is included, then use [ or ]. If not, then use ( or ). For example, the interval from -3 to 7 that includes 7 but not -3 is expressed (-3,7]. ■ For infinite intervals, use Inf for ∞ (infinity) and -Inf for - (-Infinity). For example, the infinite interval containing all points greater than or equal to 6 is expressed [6, Inf). ■ If the set includes more than one interval, they are joined using the union symbol U. For example, the set consisting of all points in (-3,7] together with all points in [-8,-5) is expressed [-8,-5) U(-3,7]. ■ If the answer is the empty set, you can specify that by using braces with nothing inside: { } ■ You can use R as a shorthand for all real numbers. So, it is equivalent to entering (-Inf, Inf). ■ You can use set difference notation. So, for all real numbers except 3, you can use R-{3} or (-Inf, 3) U(3, Inf) (they are the same). Similarly, [1,10)-{3,4} is the same as [1,3)U(3,4)U(4,10). ■ WeBWorK will not interpret [2,4] U[3,5] as equivalent to [2,5], unless a problem tells you otherwise. All sets should be expressed in their simplest interval notation form, with no overlapping intervals.
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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PLEASE ANSWER THE QUESTION ACCORDING TO INTERVAL NOTATION. AND PLEASE WRITE THE ANSWERS AT THE END TOGETHER
![Answer the following questions for the function
defined on the interval [-6.18, 0.57].
Remember that you can enter pi for π as part of your answer.
-3-л
a.) f(x) is concave down on the region(s)
2 2
f(x) =
= sin²
(-1/2)
b.) A global minimum for this function occurs at (-π,1))
c.) A local maximum for this function which is not a global maximum occurs at ((0.57,0.079)
d.) The function is increasing on the region(s) (-6.18, -π) U (0, 0.57)
Note: In some cases, you may need to give a comma-separated list of intervals, and intervals should be given in interval notation.
Using Interval Notation
■ If an endpoint is included, then use [ or ]. If not, then use ( or ). For example, the interval from -3 to 7 that includes 7 but not -3 is expressed (-3,7].
■ For infinite intervals, use Inf for ∞ (infinity) and -Inf for - (-Infinity). For example, the infinite interval containing all points greater than or equal to 6 is expressed
[6, Inf).
■ If the set includes more than one interval, they are joined using the union symbol U. For example, the set consisting of all points in (-3,7] together with all points in
[-8,-5) is expressed [-8,-5) U(-3,7].
■ If the answer is the empty set, you can specify that by using braces with nothing inside: { }
■ You can use R as a shorthand for all real numbers. So, it is equivalent to entering (-Inf, Inf).
■ You can use set difference notation. So, for all real numbers except 3, you can use R-{3} or (-Inf, 3) U(3, Inf) (they are the same). Similarly, [1,10)-{3,4} is the
same as [1,3)U(3,4)U(4,10).
■ WeBWorK will not interpret [2,4] U[3,5] as equivalent to [2,5], unless a problem tells you otherwise. All sets should be expressed in their simplest interval notation
form, with no overlapping intervals.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F12338024-533e-4da1-9dad-ffa6f519afc7%2Fc0708483-bad2-4edf-85b2-7d7d9524d78f%2Fsl2l2j8_processed.png&w=3840&q=75)
Transcribed Image Text:Answer the following questions for the function
defined on the interval [-6.18, 0.57].
Remember that you can enter pi for π as part of your answer.
-3-л
a.) f(x) is concave down on the region(s)
2 2
f(x) =
= sin²
(-1/2)
b.) A global minimum for this function occurs at (-π,1))
c.) A local maximum for this function which is not a global maximum occurs at ((0.57,0.079)
d.) The function is increasing on the region(s) (-6.18, -π) U (0, 0.57)
Note: In some cases, you may need to give a comma-separated list of intervals, and intervals should be given in interval notation.
Using Interval Notation
■ If an endpoint is included, then use [ or ]. If not, then use ( or ). For example, the interval from -3 to 7 that includes 7 but not -3 is expressed (-3,7].
■ For infinite intervals, use Inf for ∞ (infinity) and -Inf for - (-Infinity). For example, the infinite interval containing all points greater than or equal to 6 is expressed
[6, Inf).
■ If the set includes more than one interval, they are joined using the union symbol U. For example, the set consisting of all points in (-3,7] together with all points in
[-8,-5) is expressed [-8,-5) U(-3,7].
■ If the answer is the empty set, you can specify that by using braces with nothing inside: { }
■ You can use R as a shorthand for all real numbers. So, it is equivalent to entering (-Inf, Inf).
■ You can use set difference notation. So, for all real numbers except 3, you can use R-{3} or (-Inf, 3) U(3, Inf) (they are the same). Similarly, [1,10)-{3,4} is the
same as [1,3)U(3,4)U(4,10).
■ WeBWorK will not interpret [2,4] U[3,5] as equivalent to [2,5], unless a problem tells you otherwise. All sets should be expressed in their simplest interval notation
form, with no overlapping intervals.
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