NCERT Class 12 · Ch 6 Exercise 6.3 · Q7
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.3 Question 7
Find absolute extrema of 3x⁴−8x³+12x²−48x+25 on [0,3].
💡 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: Minimum −39 at x=2; maximum 25 at x=0.
- Differentiate: f′=\(12 \left(x - 2\right) \left(x^{2} + 2\right)\). The interior stationary points in this interval are \(2\).
- Evaluate every candidate: f(\(0\))=\(25\); f(\(2\))=\(-39\); f(\(3\))=\(16\).
- Comparing these values gives the absolute maximum and minimum; endpoints must be included.
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