Question

Determine the rate of change for y = √3x - 1Decreasing at an increasing rateO Increasing at a decreasing rateO Constant increasing rateO Decreasing at a decreasing rate

Answer 1

Given:

`y=√(3x-1)`

Required:

We need to find the rate of change of the given equation.

Step-by-step explanation:

Consider the given equation.

`y=√(3x-1)`

Differentiate with respect to x.

`(dy)/(dx)=(1)/(2)(1)/(√(3x-1))*3`
`(dy)/(dx)=(3)/(2√(3x-1))`

`(dy)/(dx)=(3)/(2√(3x-1))>0`
`The\text{ function is increasing}`

We know that dy/dx is the rate of the given function.

Differentiate dy/dx with respect to x.

`(d^2y)/(dc^2)=-(1)/(2)*(3)/(2(3x-1)^(3\/2))*3`
`(d^2y)/(dc^2)=(-9)/(4(3x-1)^(3\/2))<0`
`The\text{ rate is decreasing}`

The function is increasing, and the rate is decreasing.

Final answer:

Increasing at a decreasing rate.