What is the length of the sub-tangent at any | vedclass

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(B) The equation of the curve is $y = ax^3$.The length of the sub-tangent at any point $(x_1, y_1)$ is given by the formula $L = |y_1 \cdot \frac{dx}{

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$x/3$

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(B) The equation of the curve is $y = ax^3$.The length of the sub-tangent at any point $(x_1, y_1)$ is given by the formula $L = |y_1 \cdot \frac{dx}{dy}|$.First,find the derivative of the curve with respect to $x$:$\frac{dy}{dx} = 3ax^2$.Therefore,$\frac{dx}{dy} = \frac{1}{3ax^2}$.At the point $(x_1, y_1)$,the length of the sub-tangent is:$L = |y_1 \cdot \frac{1}{3ax_1^2}|$.Since the point $(x_1, y_1)$ lies on the curve,we have $y_1 = ax_1^3$.Substituting $y_1$ into the formula:$L = |ax_1^3 \cdot \frac{1}{3ax_1^2}| = |\frac{x_1}{3}|$.Thus,the length of the sub-tangent is $x/3$.

What is the length of the sub-tangent at any point on the curve $y = ax^3$?

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