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Consider the function given below:
f(x) = cos x - 2ax
Which of the following statements is true?
  • a)
    f(x) is monotonically increasing for a > 1/2
  • b)
    f(x) is monotonically increasing for a > 2
  • c)
    f(x) is monotonically decreasing for a > 1/2
  • d)
    f(x) is monotonically decreasing for a > 2
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Consider the function given below:f(x) = cos x - 2axWhich of the follo...
Consider the function:
f(x) = cos x - 2ax
f'(x) = - sin x - 2a
If this function is monotonically decreasing, then
f'(x) < 0
Therefore:
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Community Answer
Consider the function given below:f(x) = cos x - 2axWhich of the follo...
Explanation:

Understanding the function:
The given function is f(x) = cos x - 2ax.

Finding the derivative:
To determine the monotonicity of the function, we need to find its derivative. The derivative of f(x) with respect to x is f'(x) = -sin x - 2a.

Monotonicity of the function:
To analyze the monotonicity of the function, we need to look at the sign of the derivative.
- If f'(x) < 0="" for="" all="" x,="" then="" the="" function="" is="" monotonically="" />
- If f'(x) > 0 for all x, then the function is monotonically increasing.

Analysis:
Since the derivative is f'(x) = -sin x - 2a, we can see that the sign of the derivative depends on the value of a.
- For f(x) to be monotonically decreasing, we need f'(x) < 0="" for="" all="" x.="" this="" implies="" that="" -sin="" x="" -="" 2a="" />< 0="" for="" all="" x.="" />
- Since sin x lies between -1 and 1, the condition -sin x - 2a < 0="" holds="" when="" 2a="" /> 1.
- Therefore, the function f(x) = cos x - 2ax is monotonically decreasing for a > 1/2.
Therefore, the correct statement is: f(x) is monotonically decreasing for a > 1/2.
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Consider the function given below:f(x) = cos x - 2axWhich of the following statements is true?a)f(x) is monotonically increasing for a > 1/2b)f(x) is monotonically increasing for a > 2c)f(x) is monotonically decreasing for a > 1/2d)f(x) is monotonically decreasing for a > 2Correct answer is option 'C'. Can you explain this answer?
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Consider the function given below:f(x) = cos x - 2axWhich of the following statements is true?a)f(x) is monotonically increasing for a > 1/2b)f(x) is monotonically increasing for a > 2c)f(x) is monotonically decreasing for a > 1/2d)f(x) is monotonically decreasing for a > 2Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Consider the function given below:f(x) = cos x - 2axWhich of the following statements is true?a)f(x) is monotonically increasing for a > 1/2b)f(x) is monotonically increasing for a > 2c)f(x) is monotonically decreasing for a > 1/2d)f(x) is monotonically decreasing for a > 2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the function given below:f(x) = cos x - 2axWhich of the following statements is true?a)f(x) is monotonically increasing for a > 1/2b)f(x) is monotonically increasing for a > 2c)f(x) is monotonically decreasing for a > 1/2d)f(x) is monotonically decreasing for a > 2Correct answer is option 'C'. Can you explain this answer?.
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