NCERT Class 12 · Ch 6 Miscellaneous Exercise · Q1
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Miscellaneous Exercise Question 1
Show f(x)=log x/x has its maximum at x=e.
💡 Concept Hints
- Identify the domain and the inner and outer functions, or the relevant one-sided limits.
- Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.
✅ Step-by-Step Solution
Final Answer: Maximum 1/e at x=e.
- The domain is x>0; f′=(1−log x)/x².
- The derivative is positive for x<e and negative for x>e, so the unique global maximum is at e with value 1/e.
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