Example 18
Last updated at Dec. 8, 2016 by Teachoo
Transcript
Example 18 Find the equation of the tangent to the curve y = 𝑥 − 7𝑥 − 2(𝑥 − 3) at the point where it cuts the x-axis. Slope of the tangent to the curve is 𝑑𝑦𝑑𝑥 = 𝑥 − 7′ 𝑥 − 2 𝑥 − 3 − 𝑥 − 7 𝑥 − 3 + 𝑥 − 2′𝑥 − 22 𝑥 − 32 𝑑𝑦𝑑𝑥 = 1 𝑥 − 2 𝑥 − 3 − 𝑥 − 71𝑥 − 3 + 𝑥 − 2𝑥 − 22 𝑥 − 32 𝑑𝑦𝑑𝑥 = 𝑥 − 2 𝑥 − 3 − 𝑥 − 72𝑥 − 5𝑥 − 22 𝑥 − 32 𝑑𝑦𝑑𝑥 = 1 − 𝑦2𝑥 − 5𝑥 − 2𝑥 − 3 At the point where the curve cuts the x axis, y = 0 Hence the equation of the curve is 0 = 𝑥 − 7𝑥 − 2𝑥 − 3 ⇒ x = 7 The curve cuts the x – axis at point (7, 0) At point (7, 0) the slope is 𝑑𝑦𝑑𝑥7, 0 = 1 − 027−57 − 2 7 − 3 = 15 × 4 = 120 Now, the equation of the tangent at point (7, 0) with slope 120 is 𝑦 −𝑦1= 𝑚 𝑥 − 𝑥1 𝑦−0= 120 𝑥−7 20𝑦=𝑥−7 𝟐𝟎𝒚−𝒙+𝟕=𝟎
Examples
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Example 10
Example 11
Example 12
Example 13
Example 14
Example 15
Example 16
Example 17
Example 18 You are here
Example 19
Example 20
Example 21
Example 22
Example 23
Example 24
Example 25
Example 26
Example 27
Example 28
Example 29
Example 30
Example 31
Example 32
Example 33
Example 34
Example 35 Important
Example 36
Example 37 Important
Example 38 Important
Example 39
Example 40 Important
Example 41
Example 42
Example 43
Example 44
Example 45
Example 46 Important
Example 47 Important
Example 48
Example 49
Example 50
Example 51
Chapter 6 Class 12 Application of Derivatives
Serial order wise
About the Author
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.
