Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 14

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Suppose $x_{1}$ and $x_{2}$ are the point of maximum and the point of minimum respectively of the function $f (x) = 2 x^{3} - 9 a x^{2} + 12 a^{2} x + 1$ respectively, then for the equality $x_{1}^{2} = x_{2}$ to be true the value of ' $a$ ' must be

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Important Questions on Application of Derivatives

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 15

Point '

A

' lies on the curve

y = e^{- x^{2}}

and has the coordinate

(x, e^{- x^{2}})

where

x > 0

. Point

B

has the coordinates

(x, 0)

. If '

O

' is the origin, then the maximum area of the triangle

A O B

is

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 17

Let

h (x)

be a twice continuously differentiable positive function on an open interval

J

. Let

g (x) = \ln (h (x))

for each

x \in J

.

Suppose ${(h^{'} (x))}^{2} > (h^{''} (x)) h (x)$ for each $x \in J$ then

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 18

Let the equation

x - \sin x = a

has a unique root in

[- \frac{π}{2}, \frac{π}{2}]

, then

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 19

A function

f (x)

is such that

f (0) = 5

and tangent at any point

(k, f (k))

has the

x

-intercept as

(k - 3)

. Then, the value of

f (2) \cdot f (- 2)

is

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 20

Which one of the following is incorrect?

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 1

If the line

a x + b y + c = 0

is a normal to the curve

x y = 2,

then

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 2

The equation of the tangents to the curve

y = x^{4}

from the point

(2, 0)

, are given by

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>Assignment>Q 3

Suppose

f^{'} (x)

exists for each

x

and

h (x) = f (x) - {(f (x))}^{2} + {(f (x))}^{3} \forall x \in R

, then