Gradients, Tangents And Normals
Overview
Differentiation gives the gradient of a curve at any point, and from that single value you can write the equation of the tangent (the line that just touches the curve) and the normal (the line at right angles to it).
In this lesson you will use differentiation to find gradients, tangents and normals to a curve.
Objectives
- Use differentiation to find gradients, tangents and normals.
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Lesson Note
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Lesson Evaluation
Congratulations on completing the lesson on Gradients, Tangents And Normals. 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.
- For y = x^2, the gradient at x = 2 is: A. 2 B. 4 C. 8 D. 1 Answer: B
- The tangent to y = x^2 at (2, 4) is: A. y = 2x B. y = 4x - 4 C. y = 4x + 4 D. y = x - 2 Answer: B
- If a tangent has gradient 4, the normal has gradient: A. 4 B. -4 C. 1/4 D. -1/4 Answer: D
- The normal to a curve is: A. parallel to the tangent B. perpendicular to the tangent C. the same as the tangent D. horizontal Answer: B
- To find the gradient at a point you: A. integrate then substitute B. differentiate then substitute C. substitute then differentiate D. only substitute Answer: B
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