How do you find the relative extrema for $y = x^{3}$ $y=x^3$ ?

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Answer 1 · 2016-01-25T10:58:45

Differentiate and check for points which the gradient is zero or undefined.

$\frac{d y}{d x} = 3 x^{2}$ $frac{dy}{dx} = 3x^2$

$3 x^{2} = 0$ $3x^2 = 0$

$x = 0$ $x = 0$

However, the first derivative test shows that it is not an extremum, but rather an inflection point.

How do you find the relative extrema for y=x3y=x^3?