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
Last updated at Dec. 4, 2021 by Teachoo
Transcript
Question 8 The curve y = ๐ฅ^(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. ๐ ๐/๐ ๐ at (0, 0) Finding ๐ ๐/๐ ๐ ๐ฆ = ๐ฅ^(1/5) ๐ ๐/๐ ๐ = 1/5 ๐ฅ^((1/5 โ 1) ) = 1/5 ๐ฅ^((โ4)/5) = ๐/(๐๐^(๐/๐) ) Finding Slope at (0, 0) Putting ๐ = 0 in ๐๐ฆ/๐๐ฅ ๐ ๐/๐ ๐ = 1/(5 (0)^(4/5) ) = 1/0 = โ Now, Slope = tan ๐ฝ โ = tan ๐ tan ฮธ = โ โด ๐ฝ = 90ยฐ So tangent makes angle 90ยฐ 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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