AM-1764

Second derivative test

A Math · Secondary 4 · Hard · Second derivative test

The curve

y=\dfrac{x^2}{x+1}

has a stationary point at

x=0

. Find

\dfrac{d^2y}{dx^2}

and determine the nature of this stationary point.

$\dfrac{d^2y}{dx^2}=\dfrac{2}{(x+1)^3}$ ; maximum point
$\dfrac{d^2y}{dx^2}=\dfrac{2}{(x+1)^3}$ ; minimum point
$\dfrac{d^2y}{dx^2}=-\dfrac{2}{(x+1)^3}$ ; maximum point
$\dfrac{d^2y}{dx^2}=-\dfrac{2}{(x+1)^3}$ ; minimum point

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