## 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

NCERT Exemplar - MCQs

Question 1
Important

Question 2 Important

Question 3 Important

Question 4 Important

Question 5 Important

Question 6 You are here

Question 7 Important

Question 8 Important

Question 9 Important

Question 10

Question 11 Important

Question 12 Important

Question 13

Question 14

Question 15 Important

Question 16 Important

Question 17 Important

Question 1 Important

Question 2

Question 3 Important

Question 4

Question 5

Question 6 You are here

Question 7 Important

Question 8

Question 9 Important

Question 10 Important

Question 11

Question 12

Question 13

Chapter 6 Class 12 Application of Derivatives

Serial order wise

Last updated at April 16, 2024 by Teachoo

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)