1. Find the average rate of change of f(x)=x^3-9x+9:
a) from -8 to -2
b) from -1 to 1
c) from 1 to 4
a) what is averge rate of change of f (x) =x^3-9x+9 from -8 to -2?
To find the average rate of change of a function, we need to calculate the difference in the function values at the two given points and then divide it by the difference in the corresponding x-values.
For part a) of the question, we need to find the average rate of change of f(x) = x^3 - 9x + 9 from -8 to -2.
To calculate the average rate of change, we need to find the difference in the function values at the two points: f(-2) and f(-8).
First, let's substitute -2 and -8 into the function to find the function values at these points:
f(-2) = (-2)^3 - 9(-2) + 9
f(-2) = -8 + 18 + 9
f(-2) = 19
f(-8) = (-8)^3 - 9(-8) + 9
f(-8) = -512 + 72 + 9
f(-8) = -431
Now, we can calculate the difference in the function values:
Difference in function values = f(-2) - f(-8)
Difference in function values = 19 - (-431)
Difference in function values = 450
Next, we need to find the difference in the x-values, which is -2 - (-8) = -2 + 8 = 6.
Finally, we can calculate the average rate of change:
Average rate of change = Difference in function values / Difference in x-values
Average rate of change = 450 / 6
Average rate of change = 75
Therefore, the average rate of change of f(x) = x^3 - 9x + 9 from -8 to -2 is 75.
I will do a) , you do the others in the same way
f(x) = x^3 - 9x + 9
f(-2) = -8 + 18 + 9 = 19
f(-8) = -512 + 72 + 9 = -431
avg rate of change
= (f(-2) - f(-8) )/(-2 - (-8))
= (19 - (-431))/(-2 - (-8))
=450/6
= 75