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

Last updated at December 16, 2024 by

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

The curve y = x^(1/5) has at (0, 0) - Class 12 AOD [MCQ] - Teachoo - NCERT Exemplar - MCQs

part 2 - Question 6 - NCERT Exemplar - MCQs - Serial order wise - Chapter 6 Class 12 Application of Derivatives
part 3 - Question 6 - NCERT Exemplar - MCQs - Serial order wise - Chapter 6 Class 12 Application of Derivatives

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Question 6 The curve y = š‘„^(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. š’…š’š/š’…š’™ at (0, 0) Finding š’…š’š/š’…š’™ š‘¦ = š‘„^(1/5) š’…š’š/š’…š’™ = 1/5 š‘„^((1/5 āˆ’ 1) ) = 1/5 š‘„^((āˆ’4)/5) = šŸ/(šŸ“š’™^(šŸ’/šŸ“) ) Finding Slope at (0, 0) Putting š’™ = 0 in š‘‘š‘¦/š‘‘š‘„ š’…š’š/š’…š’™ = 1/(5 (0)^(4/5) ) = 1/0 = āˆž Now, Slope = tan šœ½ āˆž = tan šœƒ tan Īø = āˆž āˆ“ šœ½ = 90Ā° So tangent makes angle 90Ā° 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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