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Question

Find the length of subnormal at x= 2 on the curve y = x3.
  1. 96

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Solution

The correct option is A 96


We saw that P₁N is the length of subnormal in the given figure. It It can be easily calculated from the triangle PNP₁.

PP₁ is the y-coordinate of the point where the tangent is drawn.

θ is the slope of the tangent

From the figure tan(θ=P1NPP1)
=> P₁N = PP₁ tan θ

To calculate tan θ, we will differentiate y

=> f’(x) = 3 x2

=> f’(2) = 12 = tan θ

PP₁ = y coordinate = 23 = 8

=> Length of subnormal = PP₁ tan θ = 8 x 12 = 96

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