NCERT Class 12 · Ch 6 Miscellaneous Exercise · Q4
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Miscellaneous Exercise Question 4
Find increasing/decreasing intervals of x³+1/x³, x≠0.
💡 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: Increasing on (−∞,−1) and (1,∞); decreasing on (−1,0) and (0,1).
- f′=3x²−3/x⁴=3(x⁶−1)/x⁴.
- The denominator is positive. The numerator is positive when |x|>1 and negative when 0<|x|<1. The excluded point 0 separates the two decreasing intervals.
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