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) = x^4 - 4x^3 + 6x^2, what is f'(2)? (2019)
If f(x) = x^4 - 4x^3 + 6x^2, what is f'(2)? (2019)
Expand All
Collapse All
Practice Questions
1 question
Q1
If f(x) = x^4 - 4x^3 + 6x^2, what is f'(2)? (2019)
0
4
8
16
Show Solution
Copy
f'(x) = 4x^3 - 12x^2 + 12x; f'(2) = 4(2^3) - 12(2^2) + 12(2) = 32 - 48 + 24 = 8.
Questions & Step-by-step Solutions
1 item
Q
Q: If f(x) = x^4 - 4x^3 + 6x^2, what is f'(2)? (2019)
Solution:
f'(x) = 4x^3 - 12x^2 + 12x; f'(2) = 4(2^3) - 12(2^2) + 12(2) = 32 - 48 + 24 = 8.
Steps: 12
Show Steps
Step 1: Identify the function f(x) = x^4 - 4x^3 + 6x^2.
Step 2: Find the derivative f'(x) using the power rule. The power rule states that if f(x) = x^n, then f'(x) = n*x^(n-1).
Step 3: Apply the power rule to each term in f(x):
- For x^4, the derivative is 4*x^(4-1) = 4x^3.
- For -4x^3, the derivative is -4*3*x^(3-1) = -12x^2.
- For 6x^2, the derivative is 6*2*x^(2-1) = 12x.
Step 4: Combine the derivatives to get f'(x) = 4x^3 - 12x^2 + 12x.
Step 5: Now, substitute x = 2 into f'(x) to find f'(2).
Step 6: Calculate f'(2): f'(2) = 4(2^3) - 12(2^2) + 12(2).
Step 7: Calculate each term: 4(2^3) = 4*8 = 32, -12(2^2) = -12*4 = -48, and 12(2) = 24.
Step 8: Combine the results: 32 - 48 + 24 = 8.
Step 9: Therefore, f'(2) = 8.
Related Questions
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..
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..
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
✕
↑
