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Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeTangents & NormalsMedium2 minQB

MathematicsMediumsingle choice

Maximum no. of parallel tangents of curves $y = x^{3} - x^{2} - 2 x + 5$ and $y = x^{2} - x + 3$ is

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Answer:

Solution:

Let m be the slope of a common tangent Then $m = 2 x - 1$ and $m = 3 x^{2} - 2 x - 2$ . For every real $m$ the parabola has exactly one tangent of slope $m$ (at $x = \frac{m + 1}{2}$ ), and the cubic always has a tangent parallel to it. So, infinite common (parallel) tangents

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

⏱ 2mℹ️ Source: QB

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