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

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.