Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-2>Q 7

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If tangents are drawn from the origin to the curve $y = \sin x$ , then their points of contact lie on the curve

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Important Questions on Application of Derivatives

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-2>Q 8

Number of tangents drawn from the point

(- \frac{1}{2}, 0)

to the curve

y = e^{\{x\}}

. (Here

{}

denotes fractional part function).

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-2>Q 9

Let

f (x) = \{\begin{matrix} - x^{2}, & x < 0 \\ x^{2} + 8, & x \geq 0 \end{matrix}

Equation of tangent line touching both branches of

y = f (x)

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-2>Q 10

Minimum distance between the curves

f (x) = e^{x} & g (x) = \ln x

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-2>Q 11

The point

(s)

on the parabola

y^{2} = 4 x

which are closest to the circle,

x^{2} + y^{2} - 24 y + 128 = 0

is/are:

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-2>Q 12

If

f (x) = a^{\{a^{|x|} sgn x\}}; g (x) = a^{[a^{| x |} sgn x]}

for

a > 1, a \neq 1

and

x \in R

, where

\{\} & []

denote the fractional part and integral part functions, respectively, then which of the following statements holds good for the function

h (x)

, where

(\ln a) h (x) = (\ln f (x) + \ln g (x))

.

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-2>Q 13

If

f : [1, 10] \to [1, 10]

is a non-decreasing function and

g : [1, 10] \to [1, 10]

is a non-increasing function. Let

h (x) = f (g (x))

with

h (1) = 1

, then

h (2)

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-2>Q 14

If

f (x) = |a x - b| + c |x|

is strictly increasing at atleast one point of non-differentiability of the function where

a > 0, b > 0 and c > 0

then

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-2>Q 15

If

g (x)

is a curve which is obtained by the reflection of

f (x) = \frac{e^{x} - e^{- x}}{2}

by the line

y = x

then