On the interval I = - 2 , 2 , the function f x = x + 1 e - 1 x + 1 x x ≠ 0 0 x = 0 then which one of the following hold good?

has a maximum value equal to 3 / e

is continuous for all values of x ∈ I

On the interval I = - 2 , 2 , the function f x = x + 1 e - 1 x + 1 x x ≠ 0 0 x = 0 then which one of the following hold good?

has a maximum value equal to 3 / e

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On the interval $I = [- 2, 2],$ the function $f (x) = \{\begin{cases} {(x + 1)}^{e^{- [\begin{matrix} \frac{1}{|x|} + & \frac{1}{x} \end{matrix}]}} & (x \neq 0) \\ 0 & (x = 0) \end{cases}$ then which one of the following hold good?

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Important Questions on Application of Derivatives

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Beta Question Bank for Engineering: Mathematics>Chapter 29 - Application of Derivatives>EXERCISE-2>Q 3

The coordinates of points(s) at each of which the tangents to the curve

y = x^{3} - 3 x^{2} - 7 x + 6

cut off on the positive semi axis

O X

a line segment half that on the negative semi axis

O Y

is/are given by:

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Beta Question Bank for Engineering: Mathematics>Chapter 29 - Application of Derivatives>EXERCISE-2>Q 4

The abscissa of the point on the curve

\sqrt{x y} = a + x

, the tangent at which cuts off equal intercepts from the coordinate axes is

(a > 0)

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Beta Question Bank for Engineering: Mathematics>Chapter 29 - Application of Derivatives>EXERCISE-2>Q 6

Equation of a tangent to the curve

y \cot x = y^{3} \tan x

at the point where the abscissa is

\frac{π}{4}

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Beta Question Bank for Engineering: Mathematics>Chapter 29 - Application of Derivatives>EXERCISE-2>Q 7

Consider the curve represented parametrically by the equation

x = t^{3} - 4 t^{2} - 3 t

where

y = 2 t^{2} + 3 t - 5

where

t \in R

H

denotes the number of points on the curve where the tangent is horizontal and

V

the number of points where the tangent is vertical then-

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Beta Question Bank for Engineering: Mathematics>Chapter 29 - Application of Derivatives>EXERCISE-2>Q 8

y = f (x)

be the equation of a parabola which is touched by the line

y = x

at the point where

x = 1

. Then

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Beta Question Bank for Engineering: Mathematics>Chapter 29 - Application of Derivatives>EXERCISE-2>Q 9

At the point

P (a, a^{n})

on the graph of

y = x^{n} (n \in N)

in the first quadrant a normal is drawn. The normal intersects the

Y

-axis at the point

(0, b)

. If

\lim_{a \to 0} b = \frac{1}{2},

then

n

equal

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Beta Question Bank for Engineering: Mathematics>Chapter 29 - Application of Derivatives>EXERCISE-2>Q 10

A horse runs along a circle with a speed of

20 k m / h

. A lantern is at the centre of the circle. A fence is there along the tangent to the circle at the point at which the horse starts. The speed with which the shadow of the horse moves along the fence at the moment when it covers

\frac{1}{8}

of the circle in

k m / h

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Beta Question Bank for Engineering: Mathematics>Chapter 29 - Application of Derivatives>EXERCISE-2>Q 11

Equation of the line through the point

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

and tangent to the parabola

y = \frac{- x^{2}}{2} + 2

and secant to the curve

y = \sqrt{4 - x^{2}}

On the interval I=-2,2, the function fx=x+1e-1x+1xx≠00x=0 then which one of the following hold good?

Important Questions on Application of Derivatives

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On the interval $I = [- 2, 2],$ the function $f (x) = \{\begin{cases} {(x + 1)}^{e^{- [\begin{matrix} \frac{1}{|x|} + & \frac{1}{x} \end{matrix}]}} & (x \neq 0) \\ 0 & (x = 0) \end{cases}$ then which one of the following hold good?