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Increasing and Decreasing Functions Maths - Increasing and Decreasing Functions

Gujarat Board (GSEB) - STD 12 Science - Maths (GSEB - English Medium). 124 questions in this chapter.

Question types

Increasing and Decreasing Functions question types

124 questions across 4 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

124
Questions
4
Question groups
5
Question types
Sample Questions

Increasing and Decreasing Functions questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
Let $\phi(\text{x})=\text{f}(\text{x})+\text{f}(2\text{a}-\text{x})$ and f'(x) > 0 for all $\text{x}\in[0,\text{a}].$ Then, $\phi(\text{x}):$
  1. Increases on [0, a]
  2. Decreases on [0, a]
  3. Increases on [-a, 0]
  4. Decreases on [a, 2a]
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Q 2M.C.Q (1 Marks)1 Mark
Let f(x) = x3 -6x2 +15x + 3. Then:

  1. f(x) > 0 for all $\text{x}\in\text{R}.$

  2. f(x) > 0 for all $\text{x}\in\text{R}.$

  3. f(x) is invertible.

  4. None of these.

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Q 3M.C.Q (1 Marks)1 Mark
If the function $\text{f}(\text{x})=\frac{-\text{x}}{2}+\sin\text{x}$ defined on $\Big[\frac{-\pi}{3},\frac{\pi}{3}\Big]$ is:
  1. Increasing.
  2. Decreasing.
  3. Constant.
  4. None of these.
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Q 4M.C.Q (1 Marks)1 Mark
If the function $\text{f}(\text{x})=\cos|\text{x}|-2\text{ax}+\text{b}$ increases along entire number scale, then:
  1. $\text{a}=\text{b}$
  2. $\text{a}=\frac{1}{2}\text{b}$
  3. $\text{a}\leq-\frac{1}{2}$
  4. $\text{a}>-\frac{3}{2}$
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Q 5M.C.Q (1 Marks)1 Mark
The function $\text{f}(\text{x})=\log_\text{e}\Big(\text{x}^3+\sqrt{\text{x}^6+1}\Big)$ is of the following type:
  1. Even and increasing.
  2. Odd and increasing.
  3. Even and decreasing.
  4. Odd and decreasing.
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Q 62 Marks2 Marks
Show that $\text{f}(\text{x})=\text{x}+\cos\text{x}-\text{a}$ is an increasing function on R for all values of a.
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Q 72 Marks2 Marks
Find the values of b for which the function $\text{f}(\text{x})=\sin\text{x}-\text{b}\text{x}+\text{c}$ is a decreasing function on R.
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Q 82 Marks2 Marks
Write the set of values of a for which the function f(x) = ax + b is decreasing for all $\text{x}\in\text{R}.$
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Q 113 Marks3 Marks
Write the set of values of a for which $\text{f}(\text{x})=\cos\text{x}+\text{a}^2\text{x}+\text{b}$ is strictly increasing on R.
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Q 123 Marks3 Marks
Find the set of values of 'b' for which $\text{f}(\text{x})=\text{b}(\text{x}+\cos\text{x})+4$ is decreasing on R.
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Q 143 Marks3 Marks
Find the set of values of 'a' for which $\text{f}(\text{x})=\text{x}+\cos\text{x}+\text{ax}+\text{b}$ is increasing on R.
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Q 153 Marks3 Marks
Write the set of values of k for which $\text{f}(\text{x})=\text{k}\text{x}-\sin\text{x}$ is increasing on R.
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Q 164 Marks4 Marks
Find the intervals in which the following functions are increasing or decreasing.
f(x) = x3 - 6x2 + 9x + 15
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Q 174 Marks4 Marks
Find the intervals in which the following functions are increasing or decreasing.
$\text{f}(\text{x})=5\text{x}^{\frac{3}{2}}-3\text{x}^{\frac{5}{2}},\text{x}>0$
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Q 204 Marks4 Marks
Find the intervals in which the following functions are increasing or decreasing.
$\text{f}(\text{x})=\log(2+\text{x})-\frac{2\text{x}}{2+\text{x}},\text{x}\in\text{R}$
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