A logistic function or curve is a mathematical function having an S shape, known as sigmoid curve. The name was given by Pierre Francois Verhulst in either the year of 1844 or 1845.
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If the values of the function are all positive, then the integral IS the area under the curve.
The precision of a linear approximation is dependent on the concavity of the function. If the function is concave down then the linear approximation will lay above the curve, so it will be an over-approximation ("too large"). If the function is concave up then the linear approximation will lay below the curve, so it will be an under-approximation ("too small").
For example, the derivate of x2 is 2x; then, an antiderivative of 2x is x2. That is to say, you need to find a function whose derivative is the given function. The antiderivative is also known as the indifinite integral. If you can find an antiderivative for a function, it is fairly easy to find the area under the curve of the original function - i.e., the definite integral.
curve is an action verb
The classic "S" shaped curve that is characteristic of logistic growth.
The classic "S" shaped curve that is characteristic of logistic growth.
what letter is used to refer to the characteristic shape of the logistic growth curve
logistic growth
Logistic growth
A logistic function is a mathematical model commonly used to describe growth processes that exhibit saturation, such as population growth or the spread of diseases. It has an S-shaped curve, characterized by an initial exponential growth phase that slows as it approaches a maximum carrying capacity. The logistic function is defined by the formula ( f(x) = \frac{L}{1 + e^{-k(x - x_0)}} ), where ( L ) represents the curve's maximum value, ( k ) is the growth rate, and ( x_0 ) is the x-value of the sigmoid's midpoint. This function is widely used in various fields, including biology, economics, and statistics.
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Logistic growth curve shows a carrying capacity, where the population grows exponentially at first, then levels off as it reaches the maximum sustainable population size for the environment.
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a logistic growth curve