Find the point of inflection for the curve $y = x^{3} - 6 x^{2} + 12 x + 5$

x = 0

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x = 1

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x = - 2

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x = 2

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Solution

The correct option is B $x = 2$
$y = x^{3} - 6 x^{2} + 12 x + 5$
$\frac{d y}{d x} = 3 x^{2} - 12 x + 12 = 3 (x^{2} - 4 x + 4) = 3 (x - 2)^{2}$
$\frac{d^{2} y}{d x^{2}} = 6 (x - 2)$
for point of inflection $\frac{d^{2} y}{d x^{2}} = 0 \Rightarrow 6 (x - 2) = 0$
$\Rightarrow x = 2$
Hence $x = 2$ , is the point of inflection of the given curve.

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