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The point of inflexion of the curve $y=x^{4} $ is at

\[\begin{array}{1 1}(1)x=0&(2)x=3\\(3)x=12&(4)no \;where\end{array}\]

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Let $f(x) =x^4$
$f'(x) =4x^3$
$f'(x) =0=> 4x^3=0$
=> $x=0$ is a stationary point.
$f''(x) =12x^2$
$f'''(x) =24 x$
$f'''(0) =24 x$
The given curve $y=x^4$ has point of inflection no where
Hence 4 is the correct answer.
answered May 20, 2014 by meena.p