algebra 2 question

Question

How does one find the average rate of change? What is the average rate of change of f (x) = x^3 -9x +6 from -8 to -5
(b) -1 to 1
(c) 1 to 2

Answer 1

The average rate of change of a function over an interval is the total change divided by the size of the interval.  To find the total change, you calculate the value of the function at the end of the interval and subtract the value at the beginning of the interval.

 

So let's try the first one:

 

f(x) = x³ - 9x + 6

 

The interval is -8 to -5. 

 

f(-5) = (-5)³ - 9(-5) + 6 = -125 + 45 + 6 = -74

f(-8) = (-8)³ - 9(-8) + 6 = -512 + 72 + 5 = -435

 

So the total change over the interval is f(-5) - f(-8) = -74 - (-435) = -74 + 435 = 361

 

The length of the interval is -5 - (-8) = -5 + 8 = 3

 

So the average rate of change is 361/3, or 120 1/3

 

 

Try the same technique for b and c.