Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 46

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IMPORTANT

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Let $f : [0, 2] \to R$ be a twice differentiable function such that $f^{''} (x) > 0,$ for all $x \in [0, 2] .$ If $ϕ (x) = f (x) + f (2 - x),$ then $ϕ$ is

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Important Questions on Application of Derivatives

EASY

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IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 47

Find the intervals in which the function $f$ given by $f (x) = 2 x^{2} - 3 x$ is increasing.

HARD

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IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 48

If

x \in (0, \frac{π}{2})

, then the function

f (x) = x \sin x + \cos x + \cos^{2} x

is:

EASY

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IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 49

If normal to the curve

y = f (x)

is parallel to

x

-axis, then

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Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 50

The curve

y = x^{\frac{1}{5}}

has at

(0, 0)

EASY

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IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 51

If

y = m x + 1

is a tangent to the curve

y^{2} = 4 x

, then

m

is

EASY

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IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 52

The equation of the normal to the curve

y = \sin x

at the point

(0, 0)

is

EASY

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IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 53

The co-ordinates of the point at which the tangent to the curve

y = x^{2} - 4 x + 4

is parallel to the

x -

axis are

EASY

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IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 6 - Application of Derivatives>Exercise>Q 54

The equation of the tangent to the curve

y = x^{\frac{3}{2}}

at the origin is