Understanding ISC Mathematics Class 12 Volume 1>Chapter 7 - Applications of Derivatives>EXERCISE 7.1

HARD

12th ICSE

IMPORTANT

Earn 100

A circular cone with semi-vertical angle $45 °$ , is fixed with its axis vertical and its vertex downwards. Water is poured into the cone at the rate of $2 {cm}^{3}$ per second. Find the rate at which the depth of the water is increasing when the depth is $4 cm$ .

Important Questions on Applications of Derivatives

HARD

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 7 - Applications of Derivatives>EXERCISE 7.1

Sand is pouring from a pipe at the rate of

12 {cm}^{3} / \sec

. The falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is

4 cm

?

HARD

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 7 - Applications of Derivatives>EXERCISE 7.1

A conical vessel whose height is

4

meters and of base radius

2

meters is being filled with water at the rate of

0.75

cubic meters per minute. Find the rate at which the level of the water is rising when the depth of water is

1.5

meters.

HARD

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 7 - Applications of Derivatives>EXERCISE 7.1

Water is dripping out at the steady rate of

1 c u c m / s e c

through a tiny hole at the vertex of the conical vessel, whose axis is vertical. When the slant height of water in the vessel as

4 c m

, find the rate of decrease of slant height where the semi vertical angle of the cone is

\frac{π}{6}

.

EASY

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 7 - Applications of Derivatives>EXERCISE 7.2

What is the slope of the tangent to the curve $y = x^{3} - x$ at $x = 2$ ?

MEDIUM

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 7 - Applications of Derivatives>EXERCISE 7.2

What is the slope of the tangent to the curve

y = 3 x^{4} - 4 x

at

x = 4

?

EASY

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 7 - Applications of Derivatives>EXERCISE 7.2

What is the slope of the tangent to the curve

x^{2} + y^{2} + 3 y = 5

at the point

(1, 1)

EASY

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 7 - Applications of Derivatives>EXERCISE 7.2

What is the slope of the tangent to the curve

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

at the point whose

x

-coordinate is

3

.

EASY

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 7 - Applications of Derivatives>EXERCISE 7.2

What is the slope of the tangent to the curve

y = 3 x^{2} + 4 x

at the point whose

x

-coordinate is

- 2

?