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)
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.
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