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JEE MATHEMATICS MCQ: TANGENTS & NORMALS

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Application +4 | -1

The slope of the tangent at the point of inflection of

y=x^{3}-3 x^{2}+6 x+2009

is equal to:

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Correct option: B

3

Option B (3) is correct because the slope of the tangent at the point of inflection is found by taking the second derivative, setting it to zero to find the x-coordinate of the inflection point, and then substituting that x-value into the first derivative.

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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

y^3-3 x y+2=0

H

is the set of points on the curve

\mathrm{C}

where the tangent is parallel to

x

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)

x

-axis, then The tangents to the curve

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

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

are parallel to: