f(x)=e^x
f'(x)=e^x
Function f(x) is an exponential function. It is defined using the constant ‘e’ which is a mathematical constant that is approximately equal to 2.71828. The function is defined as:
f(x) = e^x
This means that when we input a value of x, the function will return a value that is e raised to the power of x.
For example, if x = 3, then f(x) = e^3 = 20.0855 (approx)
The graph of this function is an upward sloping curve that never touches or intersects the x-axis. As the value of x increases, the value of f(x) increases at a faster rate.
The derivative of this function is also e^x. This means that the slope of the graph at any point is equal to the value of the function at that point. The integral of this function is also e^x + C, where C is the constant of integration.
Exponential functions are commonly used in many fields such as finance, biology, physics, and engineering. They are particularly useful when we want to model situations where the rate of growth or decay is proportional to the current amount.
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