Question

Find the average rate of change of the function f(x)=1 x²-6 x-1, on the interval x ∈[0,1].

Average rate of change = __

Answer 1

The average rate of change of the function f(x)=x² - 6x - 1 on the interval x ∈ [0,1] is -5.

Step-by-step explanation:

To find the average rate of change of the function f(x) = x² - 6x - 1 on the interval x ∈ [0,1], we need to calculate the change in the function's values over the interval divided by the change in x. Let's find the function values at x = 0 and x = 1.

f(0) = (0)² - 6(0) - 1 = -1

f(1) = (1)² - 6(1) - 1 = -6

Now, we can calculate the average rate of change:

Average rate of change = (f(1) - f(0))/(1 - 0) = (-6 - -1)/(1 - 0) = -5/1 = -5