Thank you for your response. So can I say generally that if I apply some monotonic function to other, that extremes stay at same point?Chestermiller said:They just felt like its easier to differentiate the natural log of f, rather than f itself. Both f and its natural log have a maximum at the same value of v.
What are your thoughts on this?Vrbic said:Thank you for your response. So can I say generally that if I apply some monotonic function to other, that extremes stay at same point?
What are you asking me now? How or my oppinion if it is true?Chestermiller said:What are your thoughts on this?
Chet
I'm asking to see if you can reason it out mathematically.Vrbic said:What are you asking me now? How or my oppinion if it is true?
No. I just ask :)Chestermiller said:I'm asking to see if you can reason it out mathematically.
Very nice ;) It is true what I said.Chestermiller said:Suppose g(y) is a monotoically increasing function of y, and y(x) is a function of x with a maximum. Then, by the chain rule,
$$\frac{dg}{dx}=\frac{dg}{dy}\frac{dy}{dx}$$
dg/dy is always positive, so dg/dx has a zero derivative at the same location where dy/dx has a zero derivative.
The most likely speed in the Maxwell-Boltzmann distribution is the speed at which the majority of particles in a gas are moving. It is also known as the mode speed and is dependent on the temperature of the gas.
The most likely speed in the Maxwell-Boltzmann distribution can be calculated using the formula v mode = √(2kT/m), where k is the Boltzmann constant, T is the temperature in Kelvin, and m is the mass of the gas particles.
The most likely speed in the Maxwell-Boltzmann distribution is affected by the temperature of the gas, the mass of the gas particles, and the Boltzmann constant. It also depends on the type of gas and the conditions it is in.
The most likely speed in the Maxwell-Boltzmann distribution is not necessarily equal to the average speed. The most likely speed represents the peak of the distribution curve, while the average speed is the average of all speeds in the distribution. However, as the temperature increases, the most likely speed and the average speed get closer to each other.
No, the most likely speed can vary for different gas particles in the Maxwell-Boltzmann distribution. This is because the distribution takes into account the individual masses of the particles, so lighter particles will have a higher most likely speed compared to heavier particles at the same temperature.