The derivative of the function 2(f(x))^2 signifies the rate of change of attendance for each festival when the attendance is doubled.
The function 2(f(x))^2 represents doubling the attendance for each festival. To find the derivative of this function, we can apply the power rule for differentiation. The power rule states that if we have a function of the form f(x)^n, the derivative is given by n * f(x)^(n-1) * f'(x), where f'(x) is the derivative of f(x) with respect to x.
In this case, let's consider the attendance for festival A. The original attendance is 300. Doubling this attendance gives us 2 * 300 = 600. Now, let's find the derivative of (2 * 300)^2 with respect to the attendance for festival A.
Using the power rule, the derivative is 2 * 2 * 300^2 * 1 = 2400 * 300 = 720000.
Therefore, the derivative of the function 2(f(x))^2 signifies the rate of change of attendance for each festival when the attendance is doubled.
The probable question may be:
In a town, there are four major cultural festivals (A, B, C, and D) celebrated by the residents. The number of attendees for each festival is represented in the table below:
Festival Attendance
A 300
B 400
C 250
D 350
Now, let's explore the impact of doubling the attendance for each festival. If 2 times the attendance for each festival is represented by the function 2(f(x))2(f(x)), what does the derivative of this function signify in the context of cultural festivals