Find the average rate of change of the function f(x)=x^2+4x from x1=1 to x2=-7
as always, the average rate of change over an interval [a,b] is just the slope of the line joining the two points on the graph:
∆y/∆x = (f(b)-f(a))/(b-a)
so, for this one, that is
(f(1)-f(-7))/(1 - (-7)) = (5-21)/(8) = -2
f(x)=x2-1
To find the average rate of change of the function f(x) = x^2 + 4x from x1 = 1 to x2 = -7, we need to calculate the difference in the function values at these two points and divide it by the difference in the x-values.
First, let's find the function values at x1 = 1 and x2 = -7:
f(x1) = f(1) = (1)^2 + 4(1) = 1 + 4 = 5
f(x2) = f(-7) = (-7)^2 + 4(-7) = 49 - 28 = 21
Next, we calculate the difference in the function values:
Δf = f(x2) - f(x1) = 21 - 5 = 16
Now, let's calculate the difference in the x-values:
Δx = x2 - x1 = -7 - 1 = -8
Finally, we can find the average rate of change by dividing Δf by Δx:
Average rate of change = (Δf / Δx) = (16 / -8) = -2
Therefore, the average rate of change of f(x) = x^2 + 4x from x1 = 1 to x2 = -7 is -2.
To find the average rate of change of a function, we need to calculate the difference in the values of the function at two different points and divide it by the difference in the corresponding x-values.
Given the function f(x) = x^2 + 4x, we need to find the difference in the values of the function at x1 = 1 and x2 = -7.
Step 1: Calculate the value of the function at x1 = 1.
f(x1) = (1)^2 + 4(1) = 1 + 4 = 5
Step 2: Calculate the value of the function at x2 = -7.
f(x2) = (-7)^2 + 4(-7) = 49 - 28 = 21
Step 3: Calculate the difference in the function values.
f(x2) - f(x1) = 21 - 5 = 16
Step 4: Calculate the difference in the x-values.
x2 - x1 = -7 - 1 = -8
Step 5: Calculate the average rate of change.
Average rate of change = (f(x2) - f(x1)) / (x2 - x1) = 16 / -8 = -2
Therefore, the average rate of change of the function f(x) = x^2 + 4x from x1 = 1 to x2 = -7 is -2.