Question

Find the length of subnormal at x= 2 on the curve y = $x^3$.

• A. 96

Answer 1

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.

$\theta$ is the slope of the tangent

From the figure tan($\theta =\frac{P_{1}N}{P{P}_1}$)
=> P₁N = PP₁ tan $\theta$

To calculate tan $\theta$, we will differentiate y

=> f’(x) = 3 $x^2$

=> f’(2) = 12 = tan $\theta$

PP₁ = y coordinate = $2^3$ = 8

=> Length of subnormal = PP₁ tan $\theta$ = 8 x 12 = 96