Question

The length of the subtangent at any point of the curve $y=a{x}^3$ is -

• A. $x$
• B. $\frac{x}{3}$
• C. $\frac{x}{a}$
• D. $ax$

Answer 1

The correct option is B $\frac{x}{3}$

Equation of curve is, $y=a{x}^3$
$\Rightarrow \frac{dy}{dx}=3a{x}^2$
Length of subtangent $=y\times \left(\frac{dx}{dy}\right)$
$=y\times \frac{1}{3a{x}^2}=\frac{a{x}^3}{3a\times x^2}=\frac{x}{3}$
Hence, option 'B' is correct.