Achieve CUET (UG) Mathematics Practice Book>Chapter 5 - Continuity and Differentiability>Exercise>Q 31

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Let $f : R \to R$ be differentiable at $c \in R$ and $f (c) = 0$ . If $g (x) = |f (x)|$ , then at $x = c, g$ is:

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Important Questions on Continuity and Differentiability

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IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 5 - Continuity and Differentiability>Exercise>Q 32

The set of points where the function

f

given by

f (x) = | 2 x - 1 | \sin x

is differentiable are

HARD

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IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 5 - Continuity and Differentiability>Exercise>Q 33

If

f (x) = \{\begin{cases} 2 a - x, & for - a < x < a \\ 3 x - 2 a & for x \geq a \end{cases}

, then which of the following is true?

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Achieve CUET (UG) Mathematics Practice Book>Chapter 5 - Continuity and Differentiability>Exercise>Q 34

If

f (x) = \{\begin{cases} a x^{2} - b, & - 1 < x < 1 \\ \frac{1}{| x |}, & elsewhere \end{cases}

is differentiable at

x = 1

, then

HARD

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Achieve CUET (UG) Mathematics Practice Book>Chapter 5 - Continuity and Differentiability>Exercise>Q 35

The set of those points on

f (x) = x |x|

where the function differentiable is

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Achieve CUET (UG) Mathematics Practice Book>Chapter 5 - Continuity and Differentiability>Exercise>Q 36

Let

f (x - y) = f (x) \cdot g (y) - f (y) \cdot g (x)

and

g (x - y) = g (x) \cdot g (y) - f (x) \cdot g (y)

for all

x, y \in R .

If right hand derivative at

x = 0

exists for

f (x)

, then derivative of

g (x)

at

x = 0

EASY

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IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 5 - Continuity and Differentiability>Exercise>Q 37

y = e^{\sin 2 x}

, then

\frac{d y}{d x}

is

EASY

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IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 5 - Continuity and Differentiability>Exercise>Q 38

If

y = e^{3 \log x}

,then

\frac{d y}{d x} =

EASY

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IMPORTANT

Achieve CUET (UG) Mathematics Practice Book>Chapter 5 - Continuity and Differentiability>Exercise>Q 39

If

x^{y} = y^{x}

then

\frac{d y}{d x} = ?