Question

How do you find the average rate of change of `f(x)=-3x^2+2` between [-2,0]?

Answer 1

6

Explanation:

Summery:
1. Derive equation for rate of change

2. By substitution of the values of x  at the two points under 
     investigation determining the actual rate of change at 
     those point.

3. Apply the standard method of determining the mean. In this 
    case it will be

`(x_1 - x_2)/2`

  Note that rate of change is from left to right on the graph. This is 
  important!

Solution:

Assumption: your given `[-2,0]` is the "inclusive" range for `x`.
Brackets facing outwards represents "exclusive".

Let `x_1=-2`
Let `x_2=0`

Given that`" "f(x) = -3x^2+2`

The rate of change is:`" "f^'(x) = -6x`

At `x_1` the rate of change is: `(-6) times (-2) = +12`
At `x_2` the rate of change is: `(-6) times 0 = 0`

So the mean rate of change is `(12 -0)/2 = 6`