Q79.Let the function f(x) = 2x3 + (2p −7)x2 + 3(2p −9)x −6 have a maxima for some value of x < 0 and a minima for some value of x > 0 . Then, the set of all values of p is (1) ( 92 , ∞) (2) (0, 29 ) (3) (−∞, 92 ) (4) (−92 , 92 )
What This Question Tests
This question involves finding the range of a parameter 'p' such that a cubic function has a local maximum at x < 0 and a local minimum at x > 0. It tests the application of derivatives and conditions for roots of quadratic equations.
Concepts Tested
Formulas Used
f'(x) = 0 (critical points)
Conditions for roots (sum, product, discriminant)
📚 NCERT Sections This Tests
9.15 — Apply Mirror Equation And The Condition:
Physics Class 12 · Chapter 9
9.15 Apply mirror equation and the condition: (a) f < 0 (concave mirror); u < 0 (object on left) (b) f > 0; u < 0 (c) f > 0 (convex mirror) and u < 0 (d) f < 0 (concave mirror); f < u < 0 to deduce the desired result.
2.1 — Two Charges 5 × 10–8 C And –3 × 10–8 C Are Located 16 Cm Apart. At
Physics Class 11 · Chapter 2
2.1 Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
14.2 — Which Of The Statements Given In Exercise 14.1 Is True For P-Type
Physics Class 12 · Chapter 14
14.2 Which of the statements given in Exercise 14.1 is true for p-type semiconductos.
📋 Question Details
- Chapter
- Applications of Derivatives
- Topic
- Maxima and Minima
- Year
- 2023
- Shift
- 25 Jan Shift 2
- Q Number
- Q79
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 6: Applications of Derivatives
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