Q73.If the function f(x) = ( x1 ) 2x; x > 0 attains the maximum value at x = 1e then : (1) eπ < πe (2) eπ > πe (3) (2e)π > π(2e) (4) e2π < (2π)e 1
What This Question Tests
The question involves using logarithmic differentiation to find the derivative of a function with a variable base and exponent, then using the first derivative test to determine conditions for maximum value.
Concepts Tested
Formulas Used
d/dx (ln y) = (1/y) dy/dx
📚 NCERT Sections This Tests
9.23 — (A) At What Distance Should The Lens Be Held From The Card Sheet In
Physics Class 12 · Chapter 9
9.23 (a) At what distance should the lens be held from the card sheet in Exercise 9.22 in order to view the squares distinctly with the maximum possible magnifying power? (b) What is the magnification in this case? (c) Is the magnification equal to the magnifying power in this case? Explain.
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.
12.1 — (A) No Different From
Physics Class 12 · Chapter 12
12.1 (a) No different from (b) Thomson’s model; Rutherford’s model (c) Rutherford’s model (d) Thomson’s model; Rutherford’s model (e) Both the models
📋 Question Details
- Chapter
- Applications of Derivatives
- Topic
- Maxima and Minima
- Year
- 2024
- Shift
- 06 Apr Shift 2
- Q Number
- Q73
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 6: Applications of Derivatives
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