- #1
meredith
- 16
- 0
Homework Statement
f(x) = (e^x)/x. at what value of x does f(x) attain its minimum
Homework Equations
The Attempt at a Solution
f'(x) = (x)(e^x) / (e^x)
then do i set both of those to 0 and solve?
how o i do that?
im losttt
The function f(x) = (e^x)/x represents the ratio between the exponential function and the variable x. It is also known as the natural exponential function.
The function f(x) = (e^x)/x is commonly used in physics, biology, and economics to model growth and decay phenomena. It can also be used to calculate probabilities in statistics.
The domain of the function f(x) = (e^x)/x is all real numbers except for x = 0, since division by zero is undefined. The range is all positive real numbers.
To determine the minimum value of f(x) = (e^x)/x, we can take the derivative of the function and set it equal to zero. Then, we can solve for x to find the value where the function attains its minimum.
The value of x at which the function f(x) = (e^x)/x attains its minimum is approximately x = 0.36788. This can be found by taking the derivative of the function and setting it equal to zero, and then solving for x using algebra or a graphing calculator.