How do you find the average rate of change of f(x)=-3x^2+2f(x)=−3x2+2 between [-2,0]?

1 Answer
Tony B
Oct 20, 2015

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)/2x1−x22

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

Solution:

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

Let x_1=-2x1=−2
Let x_2=0x2=0

Given that" "f(x) = -3x^2+2 f(x)=−3x2+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

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