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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the derivative of a constant function f(x) = 3?
💡 Hint: Remember that constants do not change.
Question 2
Easy
Using the power rule, find the derivative of f(x) = x^4.
💡 Hint: Apply the power rule: multiply by the exponent and reduce the exponent by 1.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What does the derivative of a function represent?
- The height of the function
- The rate of change of the function
- The area under the function
💡 Hint: Consider how speed relates to distance over time.
Question 2
True or False: The derivative of a constant function is always 1.
- True
- False
💡 Hint: Think of a line with no slope.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that the derivative of f(x) = 1/x is f'(x) = -1/x^2 using the limit definition.
💡 Hint: Be careful with the algebra when combining fractions.
Question 2
Find the second derivative of f(x) = 3x^4 - 5x^2 + x.
💡 Hint: Derivatives can be taken multiple times, just apply the rules successively.
Challenge and get performance evaluation