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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the equation of the tangent line at a point P(x₁, y₁) if the slope is m?
💡 Hint: Use the point-slope form of the linear equation.
Question 2
Easy
True or False: The slope of the normal line is the negative reciprocal of the slope of the tangent line.
💡 Hint: Recall the relationship between perpendicular slopes.
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 represent?
- The area under a curve
- The rate of change at a point
- The maximum value of a function
💡 Hint: Think about how we perceive change in motion.
Question 2
True or False: A point is a local maximum if the first derivative is zero and the second derivative is positive.
- True
- False
💡 Hint: Remember the conditions for maximum and minimum.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
A rectangular garden has dimensions x and y. The area A = xy = 100. Express y in terms of x and find dimensions that minimize the perimeter.
💡 Hint: Optimize the perimeter as a function of area.
Question 2
A company's cost function is C(x) = x³ - 5x² + 8x + 15. Determine the number of units produced for minimized cost.
💡 Hint: Use both derivatives to confirm minimum value.
Challenge and get performance evaluation