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### Math Assignment Class XII Ch -06 | Application of Derivatives

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## Math Assignment Class XII Ch - 09

## Differential Equations

**Extra questions of chapter 09 Applications of Derivatives, class XII with answers and hints to the difficult questions, strictly according to the CBSE Board . Important and useful math. assignment for the students of class XII****MATHEMATICS ASSIGNMENT OF CHAPTER 06**

**STRICTLY ACCORDING TO THE PREVIOUS CBSE SAMPLE QUESTION PAPERS AND CBSE BOARD PAPERS**

## RATE OF CHANGE OF QUANTITIES

Question 1

A particle moves along the curve x2 = 2y. At what point,
ordinate increases at the same rate as abscissa increases?

Answer (1, 1/2)

Solution Hint:

Differentiating the given equation
w. r. t. t

Now putting dy/dt = dx/dt and
find the value of x.

Putting the value of x in the
given equation and find the value of y

Question 2

The side of an equilateral triangle is increasing at the
rate of 2 cm/s. At what rate is its area increasing when the side of triangle
is 20 cm?

Answer: 20**√3 cm ^{2}/s**

Question 3

Volume of sphere is increasing at the rate of 3cm^{3}/s.
Find the rate of increase of surface area, when radius is 2 cm

Answer: 3cm^{2}/s

Question 4

For the curve y = 5x – 2x^{3}. If x increases at the
rate of 2 unit/sec., find the rate of change of the slope of the curve when x =
3.

Answer: -72 unit /sec

Question 5

A man 2m high walks at a uniform speed of 6km/h away from
the lamp post 6m high. Find the rate at which the length of his shadow increases.

Answer : 3km/h

Solution Hint

AB = 6m, CD = 2m dy / dt = 6 km/h,

Let AC = y, CE = x, AE = x + y,

To find : dx/dt = ?

△ABE ~ △ CDE

∴

⇒ y = 2x

Differentiating on both side w.r.t. t we get

## INCREASING & DECREASING OF FUNCTIONS

Without using derivative show that the function f(x) = 4x^{3} – 18x^{2}
+ 27x – 7 is always increasing in R

Strictly Decreasing in (-2, 6)

Question 8

Find the intervals in which the function f(x) = x^{4 }/ 4 – x^{3} – 5x^{2} + 24x + 12
is

i) Strictly increasing ii) Strictly decreasing

Answer:

Strictly Decreasing in (-∞, 3)⋃(2, 4)

Question 9

Find the interval in which the function:

f(x) = sin^{4}x + cos^{4}x, 0 ≤ x < π/2

is strictly increasing or strictly decreasing.

Answer:

Strictly increasing in (π/4, π/2)

Strictly decreasing in (0, π/4)

Question 10

Find the intervals in which f(x) = sin3x - cos3x, 0<x<π, is strictly increasing or strictly decreasing.

Answer:

Strictly increasing in (0, π/4) ⋃ (7π/12, 11π/12)

Strictly decreasing in (π/4, 7π/12) ⋃ (11π/12, π)

Question 11

^{2}-x + 1 is neither increasing nor decreasing strictly on (-1, 1)

^{3}– 6x

^{2}- 72x + 30

Strictly increasing in (-∞, -2)⋃

Strictly Decreasing in (-2, 3)

Question 13

Find the interval in which the following functions are strictly increasing and strictly decreasing : f(x) = 2x^{3} – 12x^{2} + 18x + 5

Answer:

Strictly increasing in (-∞, 1)⋃

Strictly Decreasing in (1, 3)

Strictly increasing in

Strictly Decreasing in

Question 15

Find the intervals in which the function given by f(x) = sin3x, x∈ [0, π/2] is increasing and decreasing.

Answer

Increasing on [0, π/6]

Decreasing on [π/6, π/2]

Question 16

## MAXIMA AND MINIMA

Question 17

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