## 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 Ex.17VSAQ

## 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 < k < 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)