Question

Find the rate of change over the interval (2, 5) for the equation13) y=x-1-6-4-26A) 2/3B) 1/2C) 1/3D) 1/4

Answer 1

The rate of change over the interval is the difference in the y coordinate over the difference in x-coordinate over between the endpoints of the interval.

`\text{rate of change =}(\Delta y)/(\Delta x)`

Now, in our case

`(\Delta y)/(\Delta x)=(y(5)-y(2))/(5-2)`
`=\frac{\sqrt[]{5-1}-\sqrt[]{2-1}}{5-2}`
`=(2-1)/(5-2)=(1)/(3)`
`\therefore\text{rate of change }=(1)/(3)\text{.}`

Hence, choice C is correct.