f(x) = x³ - 9x\nwhat is the average rate of change of f over the interval 1,6?

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function (y = f(x)) over the interval ([a,b]) is (\frac{f(b)-f(a)}{b - a}). Here, (a = 1), (b=6).

Step2: Calculate (f(1)) and (f(6))

For (x = 1), (f(1)=1^{3}-9\times1=1 - 9=-8). For (x = 6), (f(6)=6^{3}-9\times6=216-54 = 162).

Step3: Substitute into the formula

(\frac{f(6)-f(1)}{6 - 1}=\frac{162-(-8)}{6 - 1}=\frac{162 + 8}{5}=\frac{170}{5})

Answer:

(34)