Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 63

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CUET (UG)

IMPORTANT

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The distance between the origin and the normal to the curve $y = e^{2 x} + x^{2}$ at $x = 0$ is

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Important Questions on Application of Derivatives

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CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 64

The length of the subtangent to the curve

x^{2} + x y + y^{2} = 7

at

(1, - 3)

is

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CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 65

The point on the curve

9 y^{2} = x^{3}

where the normal to the curve makes equal intercepts with the axes is

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CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 66

The normal to the curve

x^{2} = 4 y

passing

(1, 2)

is

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CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 67

The points on the curve

9 y^{2} = x^{3}

, where the normal to the curve makes equal intercepts with the axes are

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CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 68

The point on the curve

y = x^{3} - 11 x + 5

at which the tangent is

y = x - 11

is

(m, n)

. Find the value of

m + n

.

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CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 69

If the tangent at

(1, 1)

on

y^{2} = x (2 - x)^{2}

meets the curve again at

P

, then

P

is:

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CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 70

If the tangent to the curve,

y = x^{3} + a x - b

at the point

(1, - 5)

is perpendicular to the line,

- x + y + 4 = 0,

then which one of the following points lies on the curve?

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CUET (UG)

IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 71

Let

S

be the set of all values of

x

for which the tangent to the curve

y = f (x) = x^{3} - x^{2} - 2 x

at

(x, y)

is parallel to the line segment joining the points

(1, f (1))

and

(- 1, f (- 1)),

then

S

is equal to