Calculate the average rate of change across the interval [0,2] for the given function. Write your answer as a fraction (or improper fraction) in simplest form.

Question

i need the answer

Answer 1

Use the formula for the average rate of change to find the average rate of change of the function over the given interval

The average rate of change of a function

𝑓(𝑥) over the interval [a,b] is given by

1. f(b)−f(a)/b−a
2. Step 1

Substitute the given values (a=0, b=2) into the formula for the average rate of change.

1. f(b)-f(a)/b-a
2. f(2)-f(0)/2-0

1. Step 2

Evaluate f(2)

1. f(x)=3x²-2x+1
2. f(2)=3(2)²-2(2)+1
3. f(2)=3*4--4+1
4. f(2)=12-4+1
5. f(2)=9

1. Step 3

Evaluate f(0)

1. f(x)=3x2−2x+1
2. f(0)=3(0)2−2(0)+1
3. f(0)=0−0+1
4. 𝑓(0)=1
5. Step 4
6. Substitute the evaluated values( f(2)=9,f(0)=1) into the formula for the average rate of change.
7. f(2)−f(0)/2−0
8. 9-1/2-0
9. 8/2
10. 4

Solution

The average rate of change of the function f(x)=3x²-2x+1 over the interval is 4.