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
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Last updated at Dec. 4, 2021 by Teachoo
Question 8 The curve y = π₯^(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. π π/π π at (0, 0) Finding π π/π π π¦ = π₯^(1/5) π π/π π = 1/5 π₯^((1/5 β 1) ) = 1/5 π₯^((β4)/5) = π/(ππ^(π/π) ) Finding Slope at (0, 0) Putting π = 0 in ππ¦/ππ₯ π π/π π = 1/(5 (0)^(4/5) ) = 1/0 = β Now, Slope = tan π½ β = tan π tan ΞΈ = β β΄ π½ = 90Β° So tangent makes angle 90Β° with x-axis Thus, tangent is parallel to y-axis i.e. a vertical tangent So, the correct answer is (A)