NCERT Class 12 · Ch 6 Exercise 6.2 · Q6
NCERT Class 12 Maths · Chapter 6 Applications Of Derivatives · Exercise 6.2 Question 6
Find intervals of strict increase/decrease: (a) \(x^{2} + 2 x - 5\); (b) \(- 2 x^{2} - 6 x + 10\); (c) \(- 2 x^{3} - 9 x^{2} - 12 x + 1\); (d) \(- x^{2} - 9 x + 6\); (e) \(\left(x - 3\right)^{3} \left(x + 1\right)^{3}\)
✅ Step-by-Step Solution
Final Answer: (a) Decreasing (−∞,−1), increasing (−1,∞).; (b) Increasing (−∞,−3/2), decreasing (−3/2,∞).; (c) Decreasing (−∞,−2) and (−1,∞); increasing (−2,−1).; (d) Increasing (−∞,−9/2), decreasing (−9/2,∞).; (e) Decreasing (−∞,1), increasing (1,∞); the isolated derivative zeros −1 and 3 do not break strict monotonicity.
- (a) f′=\(2 \left(x + 1\right)\).
- Decreasing (−∞,−1), increasing (−1,∞).
- (b) f′=\(- 2 \left(2 x + 3\right)\).
- Increasing (−∞,−3/2), decreasing (−3/2,∞).
- (c) f′=\(- 6 \left(x + 1\right) \left(x + 2\right)\).
- Decreasing (−∞,−2) and (−1,∞); increasing (−2,−1).
- (d) f′=\(- 2 x - 9\).
- Increasing (−∞,−9/2), decreasing (−9/2,∞).
- (e) f′=\(6 \left(x - 3\right)^{2} \left(x - 1\right) \left(x + 1\right)^{2}\).
- Decreasing (−∞,1), increasing (1,∞); the isolated derivative zeros −1 and 3 do not break strict monotonicity.
