NCERT Class 12 · Ch 6 Exercise 6.2 · Q8
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.2 Question 8
Find intervals of increase and decrease for f(x)=\(x^{2} \left(x - 2\right)^{2}\).
💡 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 (0,1) and (2,∞); decreasing on (−∞,0) and (1,2).
- f′=4x(x−1)(x−2). The critical points are 0,1,2.
- Its signs across them are −,+,−,+. Thus the increasing intervals are (0,1) and (2,∞), and the decreasing intervals are (−∞,0) and (1,2); stationary boundary points may be included.
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