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Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeTangents & NormalsMedium2 minQB

MathematicsMediumsingle choice

The number of points on the curve $y^{3} - 3 x y + 2 = 0$ where the tangent is either horizontal or vertical is

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Answer:

Solution:

$3 y^{2} y^{'} - 3 y - 3 x y^{'} = 0 \Rightarrow y^{'} = \frac{y}{y ^{2} - x}$ $y^{'} = 0 \Rightarrow y = 0$ , no real $x$ $y^{'} = \infty \Rightarrow y^{2} = x \Rightarrow y^{3} = 1 \Rightarrow y = 1$ . The point is $(1, 1)$

Stream:JEESubject:MathematicsTopic:Application of DerivativeSubtopic:Tangents & Normals

⏱ 2mℹ️ Source: QB

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