Question

Find the location and nature of the stationary point(s) on the curve y = x^3 - 3x +2

Answer 1

Answer:

Check derivatives

$\frac{dy}{dx} = 3 {x}^{2} - 3 = 0 \\ \\ x = 1 \: and \: - 1$

So 1 and -1 are stationary points

Second derivative

$\frac{d {}^{2} y}{d {}^{2} x} = 6x$

At x = 1 , second derivative > 0 , so curve is concave upward

At x = -1 , second derivative < 0 , so curve is concave downwards

Answer 2

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