NCERT Class 12 · Ch 6 Exercise 6.3 · Q29
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.3 Question 29
Find the maximum of [x(x−1)+1]^(1/3) on 0≤x≤1.
💡 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: C: 1, at x=0 or 1.
- On [0,1], x(x−1)≤0, so x(x−1)+1≤1; its minimum is 3/4, hence the cube root is real and increasing in its argument.
- Both endpoints make the bracket 1. Thus the maximum cube root is 1.
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