Q80.Let x = 2 be a local minima of the function f(x) = 2x4 −18x2 + 8x + 12, x ∈(−4, 4). If M is local maximum value of the function f in (−4, 4), then M = (1) 12√6 −332 (2) 12√6 −312 (3) 18√6 −332 (4) 18√6 −312
What This Question Tests
The question requires finding local maximum and minimum values of a polynomial function within a given interval using the first derivative test and evaluating the function at critical points.
Concepts Tested
Formulas Used
f'(x) = 0 for critical points
Sign change of f'(x) for local extrema
📚 NCERT Sections This Tests
9.18 — For Fixed Distance S Between Object And Screen, The Lens Equation
Physics Class 12 · Chapter 9
9.18 For fixed distance s between object and screen, the lens equation does not give a real solution for u or v if f is greater than s/4. Therefore, fmax = 0.75 m.
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.
9.18 — The Image Of A Small Electric Bulb Fixed On The Wall Of A Room Is To Be
Physics Class 12 · Chapter 9
9.18 The image of a small electric bulb fixed on the wall of a room is to be obtained on the opposite wall 3m away by means of a large convex lens. What is the maximum possible focal length of the lens required for the purpose?
📋 Question Details
- Chapter
- Applications of Derivatives
- Topic
- Maxima and Minima
- Year
- 2023
- Shift
- 25 Jan Shift 1
- Q Number
- Q80
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 6: Application of Derivatives
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