First slide

Tangents and normals

Question

The point on the curve $y^{3} - 3 x y + 2 = 0$ where the tangent is horizontal is

Moderate

A

$(0, 0)$
B

$(1, 1)$
C

$(0, 1)$
D

Does not exist

Solution

Slope $= (\frac{d y}{d x}) = \frac{- (3 y)}{3 y^{2} - 3 x} = \frac{3 y}{3 y^{2} - 3 x}$
If the tangent is horizontal

$\Rightarrow slope = 0 \Rightarrow y = 0$

$\Rightarrow$ x does not exist

$∴$ Point does not exist

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