Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 40, is less than or equal to, x, is less than or equal to, 5540≤x≤55.
To find the average rate of change over the interval [40, 55], we need to calculate the change in the function value divided by the change in the input value.
The function f(x) is not provided in the table, so we cannot directly find the average rate of change from the table.
To find the average rate of change, we need to calculate the difference in the function values at x = 55 and x = 40, and divide it by the difference in the input values.
Let's assume the function f(x) is given by f(x) = 3x^2.
Using this function, we can calculate the function values at x = 40 and x = 55:
f(40) = 3(40)^2 = 3(1600) = 4800
f(55) = 3(55)^2 = 3(3025) = 9075
Then, we can calculate the average rate of change over the interval [40, 55]:
Average rate of change = (f(55) - f(40))/(55 - 40)
= (9075 - 4800)/(15)
= 4275/15
= 285
Therefore, the average rate of change of the function over the interval [40, 55] is 285.