Question

What is the average rate of change of the function f(x)=x2–5x+14 on the interval from x=3 to x=5?

Answer 1

3

Explanation:

To find the average rate of change from two points: [a, b] we generally use the slope equation, which can be represented as:
`(f(a)-f(b))/(a-b)`

So here let's first calculate f(3) and f(5)

`f(3)=(3)^2-5(3)+14\\f(3)=8\\\\f(5)=(5)^2-5(5)+14\\f(5)=14`

Now let's plug these values into the equation:
`(f(5)-f(3))/(5-3)`

To get the equation:
`\Longrightarrow (14-8)/(5-3)=(6)/(2)=3`