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

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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.**

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.