The curve y - e xy - x -0 has a vertical tangent at the pointA- 0-1B- 1-1C- No pointD- 1-0

The correct option is D (1,0) dy/dx= f_x/f_y=∞ =y e^xy 1/1 x e^xy ∴ 1 xe^xy=0 ∴ e^xy=1/x.Also e^xy=x+y ∴ x+y =1/x This relation is statisfied by (1,0) only. ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Local Maxima

The curve y -...

Question

The curve $y - e^{x y} + x = 0$ has a vertical tangent at the point

(1,1)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

No point

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(0,1)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(1,0)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D
(1,0)

$\frac{d y}{d x} = - \frac{f_{x}}{f_{y}} = \infty = \frac{y e^{x y} - 1}{1 - x e^{x y}} ∴ 1 - x e^{x y} = 0 ∴ e^{x y} = \frac{1}{x} . A l s o e^{x y} = x + y ∴ x + y = \frac{1}{x}$
This relation is statisfied by (1,0) only.

Suggest Corrections

Similar questions

Q. The curve

y - e^{x y} + x = 0

has a vertical tangent at the point

Q. The curve

y - e^{x y} + x = 0

has a vertical tangent at

Q. The curve

y + e^{x y} + x = 0

has a tangent parellel to y-axis at a point

Q. The curve given by the equation

y - e^{x y} + x = 0

has a vertical tangent at the point

Q. The curve given by

x + y = e^{x y}

has a tangent as the

y

-axis at the point

Join BYJU'S Learning Program

The curve y−exy+x=0 has a vertical tangent at the point

The correct option is D (1,0) dydx=−fxfy=∞=yexy−11−xexy∴1−xexy=0∴exy=1x.Alsoexy=x+y∴x+y=1x This relation is statisfied by (1,0) only.

The curve $y - e^{x y} + x = 0$ has a vertical tangent at the point

The correct option is D
(1,0)

$\frac{d y}{d x} = - \frac{f_{x}}{f_{y}} = \infty = \frac{y e^{x y} - 1}{1 - x e^{x y}} ∴ 1 - x e^{x y} = 0 ∴ e^{x y} = \frac{1}{x} . A l s o e^{x y} = x + y ∴ x + y = \frac{1}{x}$
This relation is statisfied by (1,0) only.