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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the slope of the tangent to the curve \( y = 3x + 2 \) at \( x = 1 \)?
💡 Hint: Use the derivative of the linear function.
Question 2
Easy
Find the point of tangency on the curve \( y = x^3 \) at \( x = 2 \).
💡 Hint: Substitute \\( x = 2 \\) into the equation.
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 is the slope of the tangent to the curve \( y = x^2 \) at \( x = 2 \)?
- 2
- 4
- 3
💡 Hint: Calculate the derivative and evaluate it.
Question 2
True or False: The equation of the tangent line can be found using any two points on the tangent.
- True
- False
💡 Hint: Think about the definition of a tangent line.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Find the equation of the tangent to \( y = 2x^3 - 5x \) at \( x = 1 \) and interpret its meaning graphically.
💡 Hint: Evaluate the function and its derivative at \\( x = 1 \\).
Question 2
Determine the location of the tangent's slope being horizontal for the function \( y = x^3 - 3x \) and find the points.
💡 Hint: Find critical points by setting the derivative equal to zero.
Challenge and get performance evaluation