Alerts
Wishlist
Cart
Sign In
Categories
Current Affairs & GK
Current Affairs
Show All Current Affairs & GK
eBooks
General Aptitude
Arithmetic Aptitude
Data Interpretation
Show All General Aptitude
General Knowledge
Basic General Knowledge
General Science
Show All General Knowledge
Medical Science
Anatomy
Biochemical Engineering
Biochemistry
Biotechnology
Microbiology
Show All Medical Science
Technical
Database
Digital Electronics
Electronics
Networking
Show All Technical
Verbal and Reasoning
Logical Reasoning
Verbal Ability
Verbal Reasoning
Show All Verbal and Reasoning
›
If f(x) is continuous on [a, b], which of the following must be true?
If f(x) is continuous on [a, b], which of the following must be true?
Expand All
Collapse All
Practice Questions
1 question
Q1
If f(x) is continuous on [a, b], which of the following must be true?
f(a) = f(b)
f(x) takes every value between f(a) and f(b)
f(x) is increasing
f(x) is decreasing
Show Solution
Copy
By the Intermediate Value Theorem, a continuous function on a closed interval takes every value between f(a) and f(b).
Questions & Step-by-step Solutions
1 item
Q
Q: If f(x) is continuous on [a, b], which of the following must be true?
Solution:
By the Intermediate Value Theorem, a continuous function on a closed interval takes every value between f(a) and f(b).
Steps: 5
Show Steps
Step 1: Understand that f(x) is a function that is continuous on the interval from a to b.
Step 2: Recognize that 'continuous' means there are no breaks, jumps, or holes in the graph of the function between a and b.
Step 3: Identify the values of the function at the endpoints: f(a) is the value at the start (a) and f(b) is the value at the end (b).
Step 4: The Intermediate Value Theorem states that if you have a continuous function, it will take every value between f(a) and f(b).
Step 5: Conclude that for any value y between f(a) and f(b), there exists at least one x in the interval [a, b] such that f(x) = y.
Related Questions
F
Find the value of tan(45°).
Question: Find the value of tan(45°).Options: 01undefined√3Correct Answer: 1Solution: tan(45°) = 1...
W
What is the value of 5C2?
Question: What is the value of 5C2?Options: 1020155Correct Answer: 10Solution: 5C2 = 5! / (2!(5-2)!)..
W
What is the derivative of f(x) = x^3 - 3x^2 + 4x - 5?
Question: What is the derivative of f(x) = x^3 - 3x^2 + 4x - 5?Options: 3x^2 - 6x + 43x^2 - 6x2x^2 -..
I
If the coordinates of points A and B are (1, 2) and (3, 4) respectively, what is
Question: If the coordinates of points A and B are (1, 2) and (3, 4) respectively, what is the dista..
F
Find the value of tan(45°) + cot(45°).
Question: Find the value of tan(45°) + cot(45°).Options: 120undefinedCorrect Answer: 2Solution: tan(..
‹
Biology (School & UG)
Chemistry (School & UG)
Civil Engineering
Commerce & Accountancy
Computer Science & IT
Current Affairs & GK
Data Structures & Algorithms
eBooks
Electrical & Electronics Engineering
English (School)
General Aptitude
General Knowledge
General Knowledge & Current Affairs
Languages & Literature
Law & Legal Studies
Major Competitive Exams
Mathematics (School)
Mechanical Engineering
Medical Science
Physics (School & Undergraduate)
Quantitative Aptitude & Reasoning
Social Science (School)
Technical
Verbal and Reasoning
Vocational & Skill Development
›
Soulshift Feedback
×
On a scale of 0–10, how likely are you to recommend
The Soulshift Academy
?
0
1
2
3
4
5
6
7
8
9
10
Not likely
Very likely
✕
↑
