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 critical points of the function f(x) = x^3 - 3x^2 + 4.
Find the critical points of the function f(x) = x^3 - 3x^2 + 4.
Expand All
Collapse All
Practice Questions
1 question
Q1
Find the critical points of the function f(x) = x^3 - 3x^2 + 4.
x = 0, 2
x = 1, 2
x = 1, 3
x = 0, 1
Show Solution
Copy
To find critical points, set f'(x) = 0. f'(x) = 3x^2 - 6x = 3x(x - 2). Critical points are x = 0 and x = 2.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the critical points of the function f(x) = x^3 - 3x^2 + 4.
Solution:
To find critical points, set f'(x) = 0. f'(x) = 3x^2 - 6x = 3x(x - 2). Critical points are x = 0 and x = 2.
Steps: 8
Show Steps
Step 1: Write down the function f(x) = x^3 - 3x^2 + 4.
Step 2: Find the derivative of the function, which is f'(x).
Step 3: Calculate the derivative: f'(x) = 3x^2 - 6x.
Step 4: Set the derivative equal to zero to find critical points: 3x^2 - 6x = 0.
Step 5: Factor the equation: 3x(x - 2) = 0.
Step 6: Solve for x by setting each factor equal to zero: 3x = 0 or x - 2 = 0.
Step 7: From 3x = 0, we get x = 0. From x - 2 = 0, we get x = 2.
Step 8: The critical points are x = 0 and x = 2.
Related Questions
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 ..
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..
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
✕
↑
