Gradients, Tangents And Normals
Akopọ
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.
Awọn Afojusun
- Use differentiation to find gradients, tangents and normals.
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- 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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Derivatives
Find the derivative of a function.
"Precalculus: Derivatives" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/precalculus/pages/12-4-derivatives. Access for free at https://openstax.org/books/precalculus/pages/1-introduction
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