NCERT Class 12 · Ch 6 Exercise 6.2 · Q18
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.2 Question 18
Prove f(x)=x³−3x²+3x−100 is increasing on R.
💡 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: Strictly increasing on R.
- Rewrite f=(x−1)³−99. The cube is strictly increasing, so its translated form is too.
- Equivalently f′=3(x−1)²≥0 and its only zero is an isolated point; it cannot create a constant interval.
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