Question 6 - NCERT Exemplar - MCQs - Chapter 6 Class 12 Application of Derivatives

Last updated at Dec. 16, 2024 by Teachoo

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

Transcript

Question 6 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 Since options are about finding tangent So, finding slope of tangent i.e. 𝒅𝒚/𝒅𝒙 at (0, 0) Finding 𝒅𝒚/𝒅𝒙 𝑦 = 𝑥^(1/5) 𝒅𝒚/𝒅𝒙 = 1/5 𝑥^((1/5 − 1) ) = 1/5 𝑥^((−4)/5) = 𝟏/(𝟓𝒙^(𝟒/𝟓) ) Finding Slope at (0, 0) Putting 𝒙 = 0 in 𝑑𝑦/𝑑𝑥 𝒅𝒚/𝒅𝒙 = 1/(5 (0)^(4/5) ) = 1/0 = ∞ Now, Slope = tan 𝜽 ∞ = tan 𝜃 tan θ = ∞ ∴ 𝜽 = 90° So tangent makes angle 90° 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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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