CBSE Class 12 Mathematics 2026 Supplementary Paper 65(B)/7 · Q273 Marksmonotonicity
CBSE Class 12 Mathematics 2026 Supplementary Paper 65(B)/7 · Question 27 (Applications Of Derivatives)
Find increasing and decreasing intervals of 1−12x−9x²−2x³. OR Find the maximum and minimum of 3x⁴−8x³+12x²−48x+25 on [0,3].
Alternative 1 3 Marks
Find increasing and decreasing intervals of 1−12x−9x²−2x³.
Answer: Increasing (−2,−1); decreasing (−∞,−2) and (−1,∞).
- Differentiate to obtain −6(x+1)(x+2).
- It is positive between the roots and negative outside.
- Read off the monotonic intervals, allowing the finite turning points as endpoints.
Alternative 2 3 Marks
Find the maximum and minimum of 3x⁴−8x³+12x²−48x+25 on [0,3].
Answer: Maximum 25 at 0, minimum −39 at 2.
- The derivative is 12(x−2)(x²+2).
- The only interior critical point is 2. The values at 0,2,3 are 25,−39,16.
- Compare the values to obtain the extrema.