A) (0, 0)
B) (1, 0)
C) (0, 1)
D) does not exist
Correct Answer: D
Solution :
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.
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