Check sibling questions

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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Transcript

Question 8 The curve y = π‘₯^(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. π’…π’š/𝒅𝒙 at (0, 0) Finding π’…π’š/𝒅𝒙 𝑦 = π‘₯^(1/5) π’…π’š/𝒅𝒙 = 1/5 π‘₯^((1/5 βˆ’ 1) ) = 1/5 π‘₯^((βˆ’4)/5) = 𝟏/(πŸ“π’™^(πŸ’/πŸ“) ) Finding Slope at (0, 0) Putting 𝒙 = 0 in 𝑑𝑦/𝑑π‘₯ π’…π’š/𝒅𝒙 = 1/(5 (0)^(4/5) ) = 1/0 = ∞ Now, Slope = tan 𝜽 ∞ = tan πœƒ tan ΞΈ = ∞ ∴ 𝜽 = 90Β° So tangent makes angle 90Β° 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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.