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
›
Find the value of x for which the function f(x) = x^3 - 6x^2 + 9x has an inflect
Find the value of x for which the function f(x) = x^3 - 6x^2 + 9x has an inflection point.
Expand All
Collapse All
Practice Questions
1 question
Q1
Find the value of x for which the function f(x) = x^3 - 6x^2 + 9x has an inflection point.
1
2
3
4
Show Solution
Copy
To find inflection points, set f''(x) = 0. f''(x) = 6x - 12. Setting 6x - 12 = 0 gives x = 2.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the value of x for which the function f(x) = x^3 - 6x^2 + 9x has an inflection point.
Solution:
To find inflection points, set f''(x) = 0. f''(x) = 6x - 12. Setting 6x - 12 = 0 gives x = 2.
Steps: 9
Show Steps
Step 1: Start with the function f(x) = x^3 - 6x^2 + 9x.
Step 2: Find the first derivative f'(x) to understand the slope of the function.
Step 3: Calculate f'(x) = 3x^2 - 12x + 9.
Step 4: Find the second derivative f''(x) to determine the concavity of the function.
Step 5: Calculate f''(x) = 6x - 12.
Step 6: Set the second derivative equal to zero: 6x - 12 = 0.
Step 7: Solve for x by adding 12 to both sides: 6x = 12.
Step 8: Divide both sides by 6 to find x: x = 2.
Step 9: The value of x for which the function has an inflection point is x = 2.
Related Questions
D
Determine the local maxima or minima of f(x) = -x^2 + 4x. (2019)
Question: Determine the local maxima or minima of f(x) = -x^2 + 4x. (2019)Options: Maxima at x=2Mini..
I
If the perimeter of a rectangle is 50 cm and the length is 15 cm, what is the wi
Question: If the perimeter of a rectangle is 50 cm and the length is 15 cm, what is the width? (2020..
F
Find the second derivative of f(x) = 4x^4 - 2x^3 + x. (2019)
Question: Find the second derivative of f(x) = 4x^4 - 2x^3 + x. (2019)Options: 48x^2 - 12x + 148x^3 ..
F
For the function f(x) = sin(x) + cos(x), what is f'(π/4)? (2023)
Question: For the function f(x) = sin(x) + cos(x), what is f\'(π/4)? (2023)Options: 0√21√2/2Correct ..
S
Solve for x: 3x - 7 = 2x + 5. (2021)
Question: Solve for x: 3x - 7 = 2x + 5. (2021)Options: 1211109Correct Answer: 12Exam Year: 2021Solut..
‹
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
✕
↑
