Green Bridge Learning Resource For Maxima And Minima

Overview

Differentiation finds the high and low points of a curve: where it stops rising and starts falling, or the reverse. This is the key to optimisation, finding the greatest area, the least cost, the maximum height.

In this lesson you will apply differentiation to find stationary points and to practical maxima and minima problems, using the first and second derivative tests to tell a maximum from a minimum.

Lesson Evaluation

Congratulations on completing the lesson on Maxima And Minima. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.

You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.

Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.

At a stationary point, dy/dx equals: A. 1 B. 0 C. the y-value D. infinity Answer: B
For y = x^3 - 3x, the stationary points are at x =: A. 0 only B. ±1 C. ±3 D. 1 and 3 Answer: B
If d^2y/dx^2 < 0 at a stationary point, it is a: A. minimum B. maximum C. point of inflexion D. root Answer: B
If d^2y/dx^2 > 0 at a stationary point, it is a: A. maximum B. minimum C. root D. asymptote Answer: B
For y = x^3 - 3x, the local maximum is at: A. (-1, 2) B. (1, -2) C. (0, 0) D. (1, 2) Answer: A