# find the average rate of change f(x)=x^3-9x+5  from5 to 8

lfryerda | Certified Educator

To find the average rate of change of a function, we need to divide the differences in y-values by the differences in x-values.

This means that

`{Delta y}/{Delta x}={y_2-y_1}/{x_2-x_1}`

`={(8^3-9(8)+5)-(5^3-9(5)+5)}/{8-5}`

`={445-85}/3`

`=120`

The average rate of change is 120.

chrisyhsun | Student

To graphically represent the “average rate of change”, we can draw a line from the point on the curve at x = 5 to the point on the curve at x = 8. After that, all we have to do is find the slope of this secant line. Before that, we have to find the y-values of the two points. Plugging in 5 to the given function gives f(5) = 125 – 45 + 5 = 85. Plugging in 8 to the given function gives f(8) = 512 – 72 + 5 = 445.

Therefore, the two points that we are working with are: (5, 85) and (8, 445). To find the slope, we divide the difference between the y values by the difference between the x values (delta y over delta x gives slope). This gives: (445 – 85) / (8 – 5) = 360 / 3 = 120. Therefore, the average rate of change of the given function from 5 to 8 is 120 units y per unit x.