Example 15 - Find point at which tangent to y = root 4x-3 - 1

Example 15 - Chapter 6 Class 12 Application of Derivatives - Part 2
Example 15 - Chapter 6 Class 12 Application of Derivatives - Part 3

  1. Chapter 6 Class 12 Application of Derivatives (Term 1)
  2. Serial order wise

Transcript

Example 15 Find the point at which the tangent to the curve ๐‘ฆ = โˆš(4๐‘ฅโˆ’3)โˆ’1 has its slope 2/3 . Given, Slope of the tangent to the curve is 2/3 We know that Slope of tangent = ๐’…๐’š/๐’…๐’™ 2/3 = ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = 2/3 ๐‘‘(โˆš(4๐‘ฅ โˆ’ 3) โˆ’ 1)/๐‘‘๐‘ฅ = 2/3 1/(2โˆš(4๐‘ฅ โˆ’ 3)) ร—4โˆ’0 = 2/3 2/โˆš(4๐‘ฅ โˆ’ 3) = 2/3 3 = โˆš(4๐‘ฅโˆ’3) โˆš(๐Ÿ’๐’™โˆ’๐Ÿ‘) = 3 Squaring both sides 4x โˆ’ 3 = 9 4x = 12 x = 3 Finding y for x = 3 ๐‘ฆ=โˆš(4๐‘ฅโˆ’3) โˆ’ 1 =โˆš(12โˆ’3)โˆ’1 =โˆš9โˆ’1 =3โˆ’1 =๐Ÿ Hence, the required point is (๐Ÿ‘, ๐Ÿ)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.