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BITSAT 2023Paper 1
Exam
BITSAT
Year
2023
Paper
Paper 1
Subject
Mathematics
Chapter
Application of Derivatives

BITSAT 2023 · Paper 1 · Mathematics · Application of Derivatives

The curve given by x+y=e^ x y has a tangent parallel to the Y-axis...

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

Options

  1. A(0,1)(0,1)
  2. B(1,0)(1,0)
  3. C(1,1)(1,1)
  4. DNone of these

Correct answer

B. (1,0)(1,0)

Step-by-step solution

∵x+y=exy\because x+y=e^{x y}
Differentiating w.r.t. xx, we get
1+\frac{d y}{d x}=e^{x y} \left[ y+x \frac{d y}{d x}\right]<br />\Rightarrow \quad dydx(1−xexy)=yexy−1\frac{d y}{d x}\left(1-x e^{x y}\right)=y e^{x y}-1
⇒ dydx=yexy−11−xexy∵dydx=\frac{d y}{d x}=\frac{y e^{x y}-1}{1-x e^{x y}} \because \frac{d y}{d x}=\infty,
as tangent is parallel to Y\mathrm{Y}-axis
⇒1−xexy=0\Rightarrow 1-x e^{x y}=0
∴xexy=1\therefore \mathrm{xe}^{\mathrm{xy}}=1
This holds, when x=1x=1 and y=0y=0
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