3.6.2 - Maxima and Minima
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Practice Questions
Test your understanding with targeted questions
Define local maximum and local minimum.
💡 Hint: Think about the hills and valleys in a graph.
What is a critical point?
💡 Hint: These points are where the slope is flat or does not exist.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What happens at a local maximum?
💡 Hint: Think of hills where you walk to the top.
True or False: A local minimum can occur if the first derivative is positive.
💡 Hint: Visualize how a curve behaves at its lowest point.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Given the function f(x) = x^4 - 8x^2 + 3, find the local maxima and minima and classify them using both the first and second derivative tests.
💡 Hint: Look out for changes in the sign of the derivative around your critical points.
What is the global maximum of the function f(x) = -x^2 + 6x - 8 on the closed interval [0, 5]?
💡 Hint: Make sure to include evaluations at the boundaries!
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