Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeTangents & NormalsMedium2 minPYQ_2023

MathematicsMediumsingle choice

The curve given by $x + y = e^{x y}$ has a tangent parallel to the Y-axis at the point

Options:

Answer:

Solution:

$∵ x + y = e^{x y}$
Differentiating w.r.t. $x$ , we get
$1 + \frac{d y}{d x} = e^{x y} [y + x \frac{d y}{d x}]$
$\Rightarrow \frac{d y}{d x} (1 - x e^{x y}) = y e^{x y} - 1$
$\Rightarrow \frac{d y}{d x} = \frac{y e ^{x y} - 1}{1 - x e ^{x y}} ∵ \frac{d y}{d x} = \infty$ ,
as tangent is parallel to $Y$ -axis
$\Rightarrow 1 - x e^{x y} = 0$
$∴ xe^{xy} = 1$
This holds, when $x = 1$ and $y = 0$

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

⏱ 2mℹ️ Source: PYQ_2023

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