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NCERT Class 12 · Ch 6 Exercise 6.3 · Q10

NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.3 Question 10

Find the maximum of 2x³−24x+107 on (i) [1,3], (ii) [−3,−1].

💡 Concept Hints

  1. Identify the domain and the inner and outer functions, or the relevant one-sided limits.
  2. Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.

✅ Step-by-Step Solution

Final Answer: (i) 89 at x=3; (ii) 139 at x=−2.
  1. Part (i):
  2. Differentiate: f′=\(6 \left(x - 2\right) \left(x + 2\right)\). The interior stationary points in this interval are \(2\).
  3. Evaluate every candidate: f(\(1\))=\(85\); f(\(2\))=\(75\); f(\(3\))=\(89\).
  4. Comparing these values gives the absolute maximum and minimum; endpoints must be included.
  5. Part (ii):
  6. Differentiate: f′=\(6 \left(x - 2\right) \left(x + 2\right)\). The interior stationary points in this interval are \(-2\).
  7. Evaluate every candidate: f(\(-3\))=\(125\); f(\(-2\))=\(139\); f(\(-1\))=\(129\).
  8. Comparing these values gives the absolute maximum and minimum; endpoints must be included.

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