Class CBSE Class 12 Mathematics Applications of Derivatives Q #931
KNOWLEDGE BASED
APPLY
2 Marks 2023 VSA
Find the maximum and minimum values of the function given by \(f(x)=5+\sin 2x\).
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Step-by-Step Solution

  1. The given function is \(f(x) = 5 + \sin 2x\).
  2. We know that the range of the sine function is \(-1 \leq \sin \theta \leq 1\) for any angle \(\theta\).
  3. Therefore, \(-1 \leq \sin 2x \leq 1\).
  4. To find the minimum value of \(f(x)\), we use the minimum value of \(\sin 2x\), which is -1. So, \(f_{min}(x) = 5 + (-1) = 4\).
  5. To find the maximum value of \(f(x)\), we use the maximum value of \(\sin 2x\), which is 1. So, \(f_{max}(x) = 5 + (1) = 6\).

Correct Answer: Maximum value: 6, Minimum value: 4

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because it requires students to apply their knowledge of trigonometric functions and their ranges to find the maximum and minimum values of the given function.
Knowledge Dimension: PROCEDURAL
Justification: The question requires a series of steps to determine the maximum and minimum values, involving understanding the range of the sine function and applying it to the given function.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's understanding of trigonometric functions and their properties, which is a core knowledge component of the syllabus.

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