Q87.Let the maximum and minimum values of −x2 −12 2 + (x −7)2, x ∈R be M and m , (√8x −4) respectively. Then M2 −m2 is equal to _________ π
What This Question Tests
This problem involves finding the maximum and minimum values of a complicated function, which can be simplified by a clever substitution. It tests algebraic manipulation skills and understanding how to apply calculus for extrema.
Concepts Tested
Formulas Used
Derivative for finding critical points (dy/dx = 0)
Second derivative test for max/min
📚 NCERT Sections This Tests
8.17 — Complete Each Synthesis By Giving Missing Starting Material, Reagent Or Products
Chemistry Class 12 · Chapter 8
8.17 Complete each synthesis by giving missing starting material, reagent or products
12.5 — A Hydrogen Atom Initially In The Ground Level Absorbs A Photon,
Physics Class 12 · Chapter 12
12.5 A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of photon.
12.7 — The Radius Of The Innermost Electron Orbit Of A Hydrogen Atom Is
Physics Class 12 · Chapter 12
12.7 The radius of the innermost electron orbit of a hydrogen atom is 5.3×10–11 m. What are the radii of the n = 2 and n =3 orbits?
📋 Question Details
- Chapter
- Applications of Derivatives
- Topic
- Maxima and Minima of functions
- Year
- 2024
- Shift
- 05 Apr Shift 2
- Q Number
- Q87
- Type
- Numerical
- NCERT Ref
- Class 12 Mathematics Ch 6: Applications of Derivatives
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