Question

F(x) = x^3- 9x
What is the average rate of change of f over the interval [1, 6]

Answer 1

Explanation:

`(f(b)-f(a))/(b-a)` This is the formula for the average rate of change

over the interval (a, b)

a and b are x values

f(a) ad f(b) think of them as y values

Start calculating f(a) and f(b) a=1 b=6

replace all x's in formula with a, (1)

f(1)=1³-9(1) = 1-9= -8 f(1) = -8

Now do : b (6)

f(6) = 6³ - 9 (6) = 216-54=162 f(6) = 162

now plug everything into your equation

`(f(6)-f(1))/(6-1) =(162- (-8))/(5) =(170)/(5) =34` average rate of change.

notice the 162 - (-8) In math there is no subtraction, and you would change it to + and when you do that you much change the sign of the next value making -8 a +8.

Hope this helps. Good luck!