Practice - Example 1
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Practice Questions
Test your understanding with targeted questions
What is a critical point?
💡 Hint: Think about where the slope of the tangent is horizontal.
What indicates a local maximum?
💡 Hint: Remember the concept of rising and falling?
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What do we call a point where a function reaches its highest value locally?
💡 Hint: Think of a hilltop versus a valley.
At a critical point, the first derivative of a function is:
💡 Hint: It indicates changes in direction.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Given the function f(x) = x^4 - 8x^3 + 18x^2, find its local maxima and minima.
💡 Hint: Check changes in signs from f' around critical points.
A farmer wants to create a rectangular pen using one side of a barn as an enclosure. If the total length of fencing available is 30m, what length and width will maximize the area?
💡 Hint: Formulate the area equation and differentiate to find critical points.
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