The curve y = x^(1/5) has at (0, 0)

(A) a vertical tangent (parallel to y-axis)

(B) a horizontal tangent (parallel to x-axis)

(C) an oblique tangent

(D) no tangent

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

Transcript

Question 8 The curve y = ๐‘ฅ^(1/5) has at (0, 0) (A) a vertical tangent (parallel to y-axis) (B) a horizontal tangent (parallel to x-axis) (C) an oblique tangent (D) no tangent Since options are about finding tangent So, finding slope of tangent i.e. ๐’…๐’š/๐’…๐’™ at (0, 0) Finding ๐’…๐’š/๐’…๐’™ ๐‘ฆ = ๐‘ฅ^(1/5) ๐’…๐’š/๐’…๐’™ = 1/5 ๐‘ฅ^((1/5 โˆ’ 1) ) = 1/5 ๐‘ฅ^((โˆ’4)/5) = ๐Ÿ/(๐Ÿ“๐’™^(๐Ÿ’/๐Ÿ“) ) Finding Slope at (0, 0) Putting ๐’™ = 0 in ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ ๐’…๐’š/๐’…๐’™ = 1/(5 (0)^(4/5) ) = 1/0 = โˆž Now, Slope = tan ๐œฝ โˆž = tan ๐œƒ tan ฮธ = โˆž โˆด ๐œฝ = 90ยฐ So tangent makes angle 90ยฐ with x-axis Thus, tangent is parallel to y-axis i.e. a vertical tangent So, the correct answer is (A)

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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.