Question

The point of inflexion on the curve $y=x^{5/3}$ will be

• A. (0, 0)
• B. (1, 0)
• C. (0, 1)
• D. does not exist

Answer 1

Answer: (D)

Given, $y=x^{5/3}$
$\Rightarrow$ $\frac{dy}{dx}=\frac{5}{3}{x}^{2/3}$
For the point of inflexion,
$\frac{dy}{dx}=0$
$\Rightarrow$ $\frac{5}{3}{x}^{2/3}=0$
$\Rightarrow$ $x=0$
$\Rightarrow$ $y=0$ So, point is (0, 0)
Now, $\frac{d^{2}y}{d{x}^2}=\frac{5}{3}.\frac{2}{3}{x}^{-1/3}$
${\left(\frac{d^{2}y}{d{x}^2}\right)}_{x=0}=0$
Hence, point of inflexion does not exist.