Quiz Details
QZ-20251029-24685
Topics:
Differentiation
Integration
Difficulty:
Level 3 - Medium
Questions:
5
Generated:
October 29, 2025 at 08:49 AM
Generated by:
Guest User
Instructions: Select an answer for each question and click "Check Answer" to see if you're correct. Then view the explanation to learn more!
1 What is the derivative of f(x) = 3x^2 + 5x - 7?
Correct Answer:
C
Explanation: The derivative of a polynomial function is found by applying the power rule. For f(x) = 3x^2 + 5x - 7, the derivative f'(x) is 6x + 5.
Explanation: The derivative of a polynomial function is found by applying the power rule. For f(x) = 3x^2 + 5x - 7, the derivative f'(x) is 6x + 5.
2 What is the integral of f(x) = 4x^3?
Correct Answer:
A
Explanation: To find the integral of 4x^3, we increase the exponent by 1 and divide by the new exponent: ∫4x^3 dx = (4/4)x^4 + C = x^4 + C.
Explanation: To find the integral of 4x^3, we increase the exponent by 1 and divide by the new exponent: ∫4x^3 dx = (4/4)x^4 + C = x^4 + C.
3 Which of the following represents the derivative of sin(x)?
Correct Answer:
A
Explanation: The derivative of sin(x) is cos(x). This is a standard result from calculus.
Explanation: The derivative of sin(x) is cos(x). This is a standard result from calculus.
4 What is the result of the integral ∫(2x + 3) dx?
Correct Answer:
A
Explanation: To integrate (2x + 3), we apply the power rule: ∫2x dx = x^2 and ∫3 dx = 3x. Therefore, ∫(2x + 3) dx = x^2 + 3x + C.
Explanation: To integrate (2x + 3), we apply the power rule: ∫2x dx = x^2 and ∫3 dx = 3x. Therefore, ∫(2x + 3) dx = x^2 + 3x + C.
5 What is the fundamental theorem of calculus primarily concerned with?
Correct Answer:
B
Explanation: The fundamental theorem of calculus establishes the connection between differentiation and integration, showing that they are inverse processes.
Explanation: The fundamental theorem of calculus establishes the connection between differentiation and integration, showing that they are inverse processes.