Question:medium

The maximum value of \(\frac{\log(x)}{x}\) is:

Show Hint

Optimization problems often require differentiation and identifying critical points.

Updated On: Nov 26, 2025

\(\frac{2}{e}\)
\(e\)
7
\(\frac{1}{e}\)

Top Questions on Differential equations

The population \( p(t) \) at time \( t \) of a certain mouse species follows the differential equation \( \frac{dp(t)}{dt} = 0.5p(t) - 450 \). If \( p(0) = 850 \), then the time at which the population becomes zero is:
- WBJEE - 2025
- Mathematics
- Differential equations
View Solution
Find the solution $ \frac{d^2y}{dm^2} - k^3 \frac{dy}{dm} = y \cos m, \quad y(0) = 1 $
- MHT CET - 2025
- Mathematics
- Differential equations
View Solution
The general solution of the differential equation \( \frac{dy}{dx} = 3x^2 \) is:
- MHT CET - 2025
- Mathematics
- Differential equations
View Solution
If $ a, b $ are roots of the equation $ x^2 - 5x + 6 = 0 $, find the value of $ a^3 + b^3 $.
- BITSAT - 2025
- Mathematics
- Differential equations
View Solution
Want to practice more? Try solving extra ecology questions todayView All Questions

Questions Asked in MHT CET exam

Which of the following has the lowest boiling point?

MHT CET - 2025
intermolecular forces

View Solution

Which of the following elements has the most electronegativity: Li, Na, K, or Rb?

MHT CET - 2025
Electronegativity

View Solution

Total pressure of the solution is 500, the partial pressure of component A is 400, and the partial pressure of component B is 575. What is the mole fraction of component B?

MHT CET - 2025
Mole concept and Molar Masses

View Solution

What is the number of unpaired electrons in Lutetium (Lu) in the +3 oxidation state?

MHT CET - 2025
Oxidation Number And Oxidation States

View Solution