Question

The table of values represents a quadratic function.

What is the average rate of change for f(x) from x = 0 to x = 10 ?

Answer 1

The average rate change is 11

Answer 2

the average rate of change for f(x) from x = 0 to x = 10 is, 21

Explanation:

Average rate(A(x)) of change of f(x) over interval [a,b] is given by:

`A(x) = (f(b)-f(a))/(b-a)`

As per the statement:

The table of values represents a quadratic function.

We have to find the average rate of change for f(x) from x = 0 to x = 10

At x = 0

⇒f(0) = -6

at x = 10

⇒f(10) = 204

Substitute these in [1] we have;

`A(x) = (f(10)-f(0))/(10-0)`

⇒
`A(x) = (204-(-6))/(10)`

⇒
`A(x)=(210)/(10)`

Simplify:

A(x) = 21

Therefore, the average rate of change for f(x) from x = 0 to x = 10 is, 21