# Chapter 17 : Increasing and Decreasing Functions - Rd Sharma Solutions for Class 12-science Maths CBSE

Your CBSE Class 12 syllabus for Maths consists of topics such as linear programming, vector quantities, determinants, etc. which lay the foundation for further education in science, engineering, management, etc. Studying differential equations will be useful for exploring subjects such as Physics, Biology, Chemistry, etc. where your knowledge can be applied for scientific investigations.

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## Chapter 17 - Increasing and Decreasing Functions Exercise Ex. 17.1

## Chapter 17 - Increasing and Decreasing Functions Exercise Ex. 17.2

Find the interval in which the following function is increasing or decreasing.

*f(x)* = 3*x*^{4}- 4*x*^{3}- 12*x*^{2} + 5

Find the interval in which the following function is increasing or decreasing.

Find the interval in which the following function is increasing or decreasing.

Find the interval in
which *f(x)* is increasing or
decreasing:

Find the interval in
which *f(x)* is increasing or
decreasing:

Find the interval in
which *f(x)* is increasing or
decreasing:

## Chapter 17 - Increasing and Decreasing Functions Exercise MCQ

The interval of increase of the function f(x)=x - e^{x} + tan (2π/7) is

- (0, ∞)
- (-∞, 0)
- (1, ∞)
- (-∞, 1)

Correct option: (b)

The function f(x) = cot^{-1}x + x increases in the interval

- (1, ∞)
- (-1, ∞)
- (-∞, ∞)
- (0, ∞)

Correct option: (c)

The function f(x)=x^{x} decreases on the interval

- (0, e)
- (0, 1)
- (0, 1/e)
- (1/e, e)

Correct option: (c)

The function f(x)=2 log (x - 2) - x^{2}+4x+1 increases on the interval

- (1, 2)
- (2, 3)
- (1, 3)
- (2, 4)

Correct option:(b)

If the function f(x) = 2x^{2} - kx + 5 is increasing on [1, 2], then k lies in the interval

- (-∞, 4)
- (4, ∞)
- (-∞, 8)
- (8, ∞)

Correct option: (a)

Let f(x)= x^{3} + ax^{2} + bx + 5 sin^{2}x be an increasing function on the set R. Then a and b satisfy

- a
^{2}- 3b - 15 > 0 - a
^{2}- 3b + 15 > 0 - a
^{2}- 3b + 15 < 0 - a > 0 and b > 0

Correct option: (c)

- even and increasing
- odd and increasing
- even and decreasing
- odd and decreasing

Correct option: (b)

If the function f(x)= 2 tan x + (2a + 1) log_{e}|sec x|+ (a-2) x is increasing on R, then

- a ∈ (1/2, ∞)
- a ∈ (-1/2, 1/2)
- a = 1/2
- a ∈ R

Correct option: (c)

- increasing on (0, π/2)
- decreasing on (0, π/2)
- increasing on (0, π/4) and decreasing on (π/4, π/2)
- None of these

Correct option: (a)

Let f(x) = x^{3} - 6x^{2} + 15x + 3. Then,

- f(x) > 0 for all x ∈ R
- f(x) > f(x + 1) for all x ∈ R
- f(x) is invertible
- f(x) < 0 for all x ∈ R

Correct option: (c)

The function f(x) = x^{2}e^{-x} is monotonic increasing when

- x ∈ R - [0, 2]
- 0 < x < 2
- 2 < x < ∞
- x < 0

Correct option: (b)

The function f(x) = cos x - 2 λ x is monotonic decreasing when

- λ > 1/2
- λ < 1/2
- λ < 2
- λ > 2

Correct option: (a)

In the interval (1, 2), function f(x)= 2| x - 1|+ 3|x - 2| is

- monotonically increasing
- monotonically decreasing
- not monotonic
- constant

Correct option: (b)

** **

Function f(x) = x^{3} - 27x + 5 is monotonically increasing when

- x < -3
- |x| > 3
- x ≤ -3
- |x| ≥ 3

Correct option: (d)

Function f(x) = 2x^{3} - 9x^{2} + 12x + 29 is monotonically decreasing when

- x < 2
- x > 2
- x > 3
- 1 < x < 2

Correct option: (d)

If the function f(x) = kx^{3} - 9x^{2} + 9x + 3 is monotonically increasing in every interval, then

- k < 3
- k ≤ 3
- k > 3
- k > 3

Correct option: (c)

- x > 0
- x < 0
- x ∈ R
- x ∈ R - {0}

Correct option: (c)

Function f(x) = |x|-|x - 1| is monotonically increasing when

- x < 0
- x > 1
- x < 1
- 0 < x < 1

Correct option: (d)

Every invertible function is

- monotonic function
- constant function
- identity function
- not necessarily monotonic function

Correct option: (a)

Every invertible function is always monotonic function.

In the interval (1, 2), function f(x) = 2|x - 1| + 3|x - 2| is

- increasing
- decreasing
- constant
- none of these

Correct option: (b)

If the function f(x) = cos|x| - 2ax + b increases along the entire number scale, then

- a = b
- a =
- a ≤
- a >

Correct option: (c)

- strictly increasing
- strictly decreasing
- neither increasing nor decreasing
- none of these

Correct option: (a)

- λ < 1
- λ > 1
- λ < 2
- λ > 2

Correct option: (d)

Function f(x) = a^{x} is increasing on R, if

- a > 0
- a < 0
- 0 < a < 1
- a > 1

Correct option: (d)

Function f(x) = log_{a }x is increasing on R, if

- 0 < a < 1
- a > 1
- a < 1
- a > 0

Correct option: (b)

Let ϕ(x) = f(x) + f(2a - x) and f''(x) > 0 for all x ∈ [0, a]. Then, ϕ(x)

- increases on [0, a]
- decreases on [0, a]
- increases on [-a, 0]
- decreases on [a, 2a]

Correct option: (b)

If the function f(x) = x^{2} - kx + 5 is increasing on [2, 4], them

- k ∈ (2, ∞)
- k ∈ (-∞, 2)
- k ∈ (4, ∞)
- k ∈ (-∞, 4)

Correct option: (d)

The function f(x) = -x/2 + sin x defined on [-π/3, π/3] is

- increasing
- decreasing
- constant
- none of these

Correct option: (a)

If the function f(x) = x^{3} - 9k x^{2} + 27x + 30 is increasing on R, then

- -1 ≤ k < 1
- K < -1 or k > 1
- 0 < k < 1
- -1 < k < 0

Correct option: (a)

NOTE: Option (a) should be -1

The function f(x) = x^{9} + 3x^{7} + 64 is increasing on

(a) R

(b) (-∞, 0)

(c) (0, ∞)

(d) R_{0}

Correct option: (a)

## Chapter 17 - Increasing and Decreasing Functions Exercise Ex.17VSAQ

## Why CBSE Class 12 Science Maths solutions are important?

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