Question

Estimate the average rate of change between x = 0 and x = 2 for the function shown

A. 4

B. 5

C. 10

D. 11

Answer 1

A. 4 is the correct answer

Explanation:

Answer 2

4

Explanation:

Let the function given be f(x) = x³

The formula for calculating the average rate of change is expressed by:

f'(x) =
`(f(x+h)-f(x))/(h)`

If f(x) = x³

f(x+h) = (x=h)³

substitute the functions in the formula

`f'(x) = ((x+h)^3-x^3)/(h)\\f'(x) = ((x^3+3xh^2+3hx^2+h^3)-x^3)/(h)\\f'(x) = (3xh^2+3hx^2+h^3)/(h)\\f'(x) = (h(3xh+3x^2+h^2))/(h)\\f'(x) = 3xh+3x^2+h^2`

Since h = x₂-x₁ and x = 0

`f'(x) = 3(0)(2-0)+3(0)^2+(2-0)^2\\f'(x) = 0+0+2^2\\f'(x) = 4\\`

Hence the average rate of change is 4