find the average rate of change between f(-4) and f(-1) in the function f(x)= x^2+2x-8
that would be
(f(-1)-f(-4))/(-1 - -4)
= (-9-0)/3
= -3
See the graphs at
http://www.wolframalpha.com/input/?i=plot+y%3Dx%5E2%2B2x-8%2Cy%3D-3x+-+12+for+-5+%3C%3D+x+%3C%3D+0
To find the average rate of change between two points, we need to calculate the difference in the function values and divide it by the difference in the x-values.
First, let's find the function values at x = -4 and x = -1:
f(-4) = (-4)^2 + 2(-4) - 8
= 16 - 8 - 8
= 0
f(-1) = (-1)^2 + 2(-1) - 8
= 1 - 2 - 8
= -9
The difference in the function values is f(-1) - f(-4) = -9 - 0 = -9.
Now, let's calculate the difference in the x-values: -1 - (-4) = 3.
To find the average rate of change, we divide the difference in the function values by the difference in the x-values:
average rate of change = (f(-1) - f(-4)) / (-1 - (-4))
= -9 / 3
= -3
Therefore, the average rate of change between f(-4) and f(-1) in the function f(x) = x^2 + 2x - 8 is -3.
To find the average rate of change between two points on a function, we need to calculate the difference in the function values at those points and then divide by the difference in their corresponding x-values.
In this case, the function is f(x) = x^2 + 2x - 8, and we are interested in finding the average rate of change between f(-4) and f(-1).
First, let's find the value of f(-4):
f(-4) = (-4)^2 + 2(-4) - 8
= 16 - 8 - 8
= 0
Next, let's find the value of f(-1):
f(-1) = (-1)^2 + 2(-1) - 8
= 1 - 2 - 8
= -9
The difference in function values is -9 - 0 = -9.
Now, let's calculate the difference in their corresponding x-values:
-1 - (-4) = 3
Finally, we divide the difference in function values (-9) by the difference in x-values (3) to get the average rate of change:
Average rate of change = (-9) / (3)
= -3
Therefore, the average rate of change between f(-4) and f(-1) in the function f(x) = x^2 + 2x - 8 is -3.