JEE MATHEMATICS MCQ: TANGENTS & NORMALS

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Application +4 | -1

If the tangent to the curve

y = f\left( x \right) = x{\log _e}x,\left( {x > 0} \right)

at a point

\left( {c,f\left( c \right)} \right)

is parallel to the line segment joining to the points(1,0) and (e, e) then c=

View answer and explanation

Correct option: B

{e^{\left( {\frac{1}{{e - 1}}} \right)}}

Option B (e^(1/(e-1))) is correct because the derivative of the function at point c must equal the slope of the line segment joining the two points, which can be solved for c.

More Questions from TANGENTS & NORMALS

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The complete set of value of '

a

' for which there exists at least one line that is tangent to the graph of the curve

y=x^3-a x

at one point and normal to the graph at another point is given by The point of intersection of the tangents drawn to the curve

x^2 y=1-y

at the points where it is met by the curve

x y=1-y

, is given by Let

C

be the curve

y^3-3 x y+2=0

. If

H

is the set of points on the curve

\mathrm{C}

where the tangent is parallel to

x

-axis and

V

is the set of points on

C

where the tangent is parallel to

y

-axis, then The curve

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

has a vertical tangent at the point: If normal to the curve

y = f\left( x \right)

is parallel to

x

-axis, then The tangents to the curve

x = a\left( {\theta - \sin \theta } \right),\;y = a\left( {1 + \cos \theta } \right)

at the points

\theta = \left( {2k + 1} \right)\pi ,\;k \in Z

are parallel to: