RD Sharma - Mathematics (Volume 1)

Book: RD Sharma - Mathematics (Volume 1)

Chapter: 17. Increasing and Decreasing Functions

Subject: Maths - Class 12th

Q. No. 11 of MCQ

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11

Mark the correct alternative in the following:

The function f(x) = x2 e-x is monotonic increasing when


f(x) = x2 e-x


=xe-x(2-x)=f’(x)


for


f’(x)=0


x2 e-x=0


x(2-x)=0


x=2,x=0


f(x) is increasing in (0,2)

Chapter Exercises

Exercise 17.1
Exercise 17.2
MCQ

More Exercise Questions

1

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The interval of increase of the function f(x) = x – ex + tan is
2

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The function f(x) = cos–1 x + x increases in the interval.
3

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The function f(x) = xx decreases on the interval.
4

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The function f(x) = 2log(x – 2) – x2 + 4x + 1 increases on the interval.
5

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If the function f(x) = 2x2 – kx + 5 is increasing on [1, 2], then k lies in the interval.
6

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Let f(x) = x3 + ax2 + bx + 5 sin2x be an increasing function on the set R. Then, a and b satisfy.
7

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The function is of the following types:
8

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If the function f(x) = 2tanx + (2a + 1) loge |sec x| + (a – 2) x is increasing on R, then
9

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Let f(x) = tan–1 (g(x)), where g(x) is monotonically increasing for Then, f(x) is
10

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Let f(x) = x3 – 6x2 + 15x + 3. Then,
11

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The function f(x) = x2 e-x is monotonic increasing when
12

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Function f(x) = cosx – 2λ x is monotonic decreasing when
13

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In the interval (1, 2), function f(x) = 2 |x – 1|+3|x – 2| is
14

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Function f(x) = x3– 27x +5 is monotonically increasing when
15

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Function f(x) = 2x3 – 9x2 + 12x + 29 is monotonically decreasing when
16

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If the function f(x) = kx3 – 9x2 + 9x + 3 is monotonically increasing in every interval, then
17

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f(x) = 2x – tan–1 x – logis monotonically increasing when
18

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Function f(x) = |x| – |x – 1| is monotonically increasing when
19

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Every invertible function is
20

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In the interval (1, 2), function f(x) = 2|x – 1|+3 |x – 2| is
21

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If the function f(x) = cos|x| – 2ax + b increases along the entire number scale, then
22

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The function is
23

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The function is increasing, if
24

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Function f(x) = ax is increasing or R, if
25

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Function f(x) = loga x is increasing on R, if
26

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Let ϕ(x) = f(x) + f(2a – x) and f’’(x) > 0 for all xϵ[0, a]. The, ϕ(x)
27

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If the function f(x) = x2 – kx + 5 is increasing on [2, 4], then
28

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The function defined on is
29

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If the function f(x) = x3 – 9k x2 + 27x + 30 is increasing on R, then
30

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The function f(x) = x9 + 3x7 + 64 is increasing on

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