Comprehensive Guide to AP EAPCET Mathematics>Chapter 10 - Application of Derivatives - I>Exercise 1>Q 2

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The curve represented parametrically by the equations $x = 2 lncot t + 1$ and $y = \tan t + \cot t$

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Important Questions on Application of Derivatives - I

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Comprehensive Guide to AP EAPCET Mathematics>Chapter 10 - Application of Derivatives - I>Exercise 1>Q 3

Function

f (x) = x^{3} - 27 x + 5

is monotonic increasing when

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Comprehensive Guide to AP EAPCET Mathematics>Chapter 10 - Application of Derivatives - I>Exercise 1>Q 4

Function

f (x) = \cos x - 2 λ x

is monotonic decreasing when

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Comprehensive Guide to AP EAPCET Mathematics>Chapter 10 - Application of Derivatives - I>Exercise 1>Q 5

If

f (x) = \{\begin{cases} \sin \frac{π x}{2}, 0 \leq x < 1 \\ 3 - 2 x, x \geq 1 \end{cases}

, then

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Comprehensive Guide to AP EAPCET Mathematics>Chapter 10 - Application of Derivatives - I>Exercise 1>Q 6

If

f (x) = \{\begin{cases} x^{2}, & x \leq 0 \\ 2 \sin x, & x > 0 \end{cases}

, then

x = 0

is

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Comprehensive Guide to AP EAPCET Mathematics>Chapter 10 - Application of Derivatives - I>Exercise 1>Q 7

The equation of tangent to the curve

y = \sin x

at the point

(π, 0)

is

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Comprehensive Guide to AP EAPCET Mathematics>Chapter 10 - Application of Derivatives - I>Exercise 1>Q 8

The function

f (x) = \cot^{- 1} x + x

increases in the interval

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Comprehensive Guide to AP EAPCET Mathematics>Chapter 10 - Application of Derivatives - I>Exercise 1>Q 9

A curve

y = f (x)

passes through the point

(4, 3)

and the normal to the curve at the point happens to be a tangent to the circle

x^{2} + y^{2} = 25

. The value of

f^{'} (4)

is

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Comprehensive Guide to AP EAPCET Mathematics>Chapter 10 - Application of Derivatives - I>Exercise 1>Q 10

The largest interval in which

f (x) = 2 \sin x + \tan x - 3 x

increases is