Question

# Find the length of subnormal at  x= 2 on the curve y = x3. ___

Solution

## We saw that P₁N is the length of subnormal in the given figure. It It can be easily calculated from the triangle P₁NP. PP₁ is the y-coordinate of the point where the tangent is drawn. θ is the slope of the tangent θ From the figure tan θ=P1NPP1 ⇒P1N=PP1tanθ 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 = PP1tanθ=8×12=96

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