20E Equations of Tangents, 20F Normals to Curves

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Presentation transcript:

20E Equations of Tangents, 20F Normals to Curves Unit 5: Introduction to Differential Calculus 20E, 20F 5/9/2019 11:32 PM

Tangents to Curves 20E, 20F 5/9/2019 11:32 PM

Tangents to Curves Copy 1. Identify the function and point of tangency. 2. Find the function’s derivative. 3. Use the derivative to find the tangent’s gradient. 4. Determine the tangent using its gradient and point of tangency. Find the function’s tangent at the point where and also where Tangents do not have to be slanted. When would a function have horizontal tangents? 20E, 20F 5/9/2019 11:32 PM

Normals to Curves 1. Identify the function and point of tangency. 2. Find the function’s derivative. 3. Use the derivative to find the tangent’s gradient. To find the NORMAL at a point: Steps 1-3 of finding the tangent. 5. Determine the normal using the negative reciprocal of the tangent’s gradient and point of tangency. Copy 20E, 20F 5/9/2019 11:32 PM

Animation 20E, 20F 5/9/2019 11:32 PM

Practice p. 575: 9, 11(a)(c), 13, 15, 16 p. 578: 1(d)(e)(h), 2(b), 3(a)(b), 4 p. 581: 1(a)(d), 2, 4(b), 5 Read and follow all instructions. List the page and problem numbers alongside your work and answers in your notes. Use the back of the book to check your answers. Copy 20E, 20F 5/9/2019 11:32 PM