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Binder12345
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Homework Statement
given the formula m=n*e^(-nt) show that the maximum of this curve is at m=1/(t*e^(1)).
2. The attempt at a solution
I can show this graphically but I am curious if it is possible to do it by hand?
You must be differentiating the expression wrt n incorrectly. You need the product rule. If still stuck, please post all your working.Binder12345 said:That all makes sense my issue is how do I get the e^1 in the denominator? because isn't e^(-nt)= 0 a non real answer?
Sorry was going to edit and accidentally deleted :haruspex said:You must be differentiating the expression wrt n incorrectly. You need the product rule. If still stuck, please post all your working.
Then you are going wrong substituting n=1/t into the original equation.Binder12345 said:missing my e^1 in the denominator though
Yup that is exactly what I was doing wrong! :\haruspex said:Then you are going wrong substituting n=1/t into the original equation.
The maximum value of an exponential function depends on the specific function and its parameters. In general, exponential functions have a maximum value of infinity as the function continues to increase without bound.
To find the maximum point of an exponential function, you can take the derivative of the function and set it equal to zero. Then, solve for the input value that makes the derivative equal to zero. This input value will correspond to the maximum point on the function.
No, an exponential function can only have one maximum point. This is because the function increases without bound and does not have any local minima or maxima.
The base of an exponential function can affect the maximum value by either increasing or decreasing the steepness of the function's growth. A larger base will result in a steeper increase and a smaller base will result in a slower increase. However, the maximum value will still be infinity.
No, the maximum value of an exponential function cannot be negative. This is because the function always increases and does not have any local minima or maxima. The minimum value of an exponential function can be negative, but not the maximum value.