NCERT Class 12 · Ch 6 Exercise 6.3 · Q4
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.3 Question 4
Prove eˣ, log x and x³+x²+x+1 have no maxima or minima on their natural domains.
💡 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: No local or absolute extrema on their domains.
- Their derivatives are eˣ>0, 1/x>0 for x>0, and 3x²+2x+1=3(x+1/3)²+2/3>0.
- Each function is strictly increasing on its open domain. Every point has nearby points with both larger and smaller values.
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