NCERT Class 12 · Ch 6 Exercise 6.3 · Q2
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.3 Question 2
Find maximum/minimum values: (i) |x+2|−1; (ii) −|x+1|+3; (iii) sin 2x+5; (iv) |sin 4x+3|; (v) x+1, −1<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: (i) min −1, no max; (ii) max 3, no min; (iii) min 4, max 6; (iv) min 2, max 4; (v) neither (infimum 0, supremum 2).
- (i) |x+2|≥0, with equality at −2; (ii) |x+1|≥0, with equality at −1.
- (iii) −1≤sin 2x≤1; both endpoints occur.
- (iv) sin 4x+3 is always positive, so absolute value changes nothing; its range is [2,4].
- (v) The range is the open interval (0,2). Neither endpoint is attained, hence no maximum or minimum.
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