What is the average rate of change for the function f(x) = x^3 − 6x^2 + 4x +7 over the interval 0≤x≤5?
To find the average rate of change for a function over an interval, we need to calculate the difference in the values of the function at the endpoints of the interval and divide it by the difference in the values of x at those endpoints.
In this case, we want to find the average rate of change for the function f(x) = x^3 − 6x^2 + 4x +7 over the interval 0≤x≤5. So, we need to evaluate the function at the endpoints of the interval (0 and 5) and calculate the difference between those values.
First, let's find the value of the function at x = 0:
f(0) = (0)^3 − 6(0)^2 + 4(0) + 7 = 7
Next, let's find the value of the function at x = 5:
f(5) = (5)^3 − 6(5)^2 + 4(5) + 7
= 125 − 150 + 20 + 7
= 2
Now that we have the function values at the endpoints, we can calculate the average rate of change:
Average rate of change = (change in function values)/(change in x values)
= (f(5) - f(0))/(5 - 0)
= (2 - 7)/(5 - 0)
= -5/5
= -1
Therefore, the average rate of change for the function f(x) = x^3 − 6x^2 + 4x + 7 over the interval 0≤x≤5 is -1.
you gotta help me yall
that is just the slope of the secant line over the interval:
(f(5)-f(0))/(5-0)
but what do i plug that into??
You don't plug it into anything. It's just a calculation.
f(5) = 2
now find f(0) and finish it up