Quiz
Sign In
Review the average rate of change formula.
See solution.
We are asked to compare the average rates of change for the functions g(x) and h(x) over the interval x= 0 to x= 3. To do so, we will calculate each of the average rates of change one at a time.
We are given the graph of a square root function g(x).
Substitute values
Subtract terms
Calculate quotient
Next, we will find the average rate of change of the cube root function h(x) over the same interval, [ 0, 3]. h(x) = sqrt(32x) Let's apply the same formula one more time. Average Rate of Change = h( x_2)-h( x_1)/x_2- x_1 This time we will need to calculate h( 3) and h( 0) before we can find the average rate of change.
| Substitution | Result | |
|---|---|---|
| h(3) | sqrt(3/2( 3)) | ≈ 1.65 |
| h(0) | sqrt(3/2( 0)) | |
| h(3)-h(0) | 1.65- | ≈ 1.65 |
| h(3)-h(0)/3-0 | 1.65/3 | ≈ 0.55 |
The average rate of change of h(x) over the given interval is about 0.55.
Finally, let's compare the average rates of change. 1 > ≈0.55 We can conclude that the average rate of change of the square root function g(x) is greater than average rate of change of the cube root function h(x) over the interval [ 0, 3].