NCERT Class 12 · Ch 6 Exercise 6.3 · Q1
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.3 Question 1
Find maximum/minimum values, if any: (i) (2x−1)²+3; (ii) 9x²+12x+2; (iii) −(x−1)²+10; (iv) x³+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 3 at 1/2, no max; (ii) min −2 at −2/3, no max; (iii) max 10 at 1, no min; (iv) neither.
- (i) A square is nonnegative; it is zero at x=1/2 and unbounded above.
- (ii) Complete the square: 9(x+2/3)²−2. Its minimum is −2; it is unbounded above.
- (iii) The nonpositive term −(x−1)² gives a maximum 10 and no lower bound.
- (iv) x³+1 is strictly increasing and unbounded in both directions.
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