Finding the Point of Maximum Growth Rate for the Logistic Function f(x) in Math

Let f(x)=24/1 + 3e^−1.3x . What is the point of maximum growth rate for the logistic function f(x) ?Round your answer to the nearest hundredth.

To find the point of maximum growth rate for the logistic function f(x), we can take the derivative of f(x) with respect to x and set it equal to zero

To find the point of maximum growth rate for the logistic function f(x), we can take the derivative of f(x) with respect to x and set it equal to zero. The maximum growth rate occurs at the point where the rate of change is greatest, which corresponds to the maximum value of the derivative.

So, let’s find the derivative of f(x):

f(x) = 24/1 + 3e^(-1.3x)
f'(x) = 0 + 3 * (-1.3) * e^(-1.3x) [Using chain rule]

To find the maximum growth rate, we need to find the x-value where f'(x) equals zero. Setting f'(x) = 0:

3 * (-1.3) * e^(-1.3x) = 0

Since the exponential function e^(anything) is never zero, we can conclude that the only way for the expression to equal zero is if the coefficient (-1.3) is zero. Therefore, we solve for x:

-1.3x = 0
x = 0

So, the point of maximum growth rate for the logistic function f(x) is at x = 0.

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