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:

$y=\sqrt{3x-1}$

Required:

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

Explanation:

Consider the given equation.

$y=\sqrt{3x-1}$

Differentiate with respect to x.

$\frac{dy}{dx}=\frac{1}{2}\frac{1}{\sqrt{3x-1}}\times3$$\frac{dy}{dx}=\frac{3}{2\sqrt{3x-1}}$

$\frac{dy}{dx}=\frac{3}{2\sqrt{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.

$\frac{d^2y}{dc^2}=-\frac{1}{2}\times\frac{3}{2(3x-1)^{3\/2}}\times3$$\frac{d^2y}{dc^2}=\frac{-9}{4(3x-1)^{3\/2}}<0$$The\text{ rate is decreasing}$

The function is increasing, and the rate is decreasing.

Final answer:

Increasing at a decreasing rate.