Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Determine if the equation describes an increasing or decreasing function or neither.$$r(x)=\sqrt{2-5 x}$$

Decreasing

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 1

Inverse Functions

Campbell University

Baylor University

University of Michigan - Ann Arbor

Lectures

01:09

Determine whether each fun…

00:47

Determine if the equation …

01:39

02:03

01:34

00:40

Determine whether the foll…

01:37

00:50

Determine whether the func…

01:14

01:17

01:33

01:35

Inspect the graph of the f…

01:32

So one way we can determine if a function is increasing or decreasing is by taking the derivative of it. And if the derivative is always positive, it will be increasing. And if the derivative is always negative, then it will be decreasing. So let's go and take the derivative of this and see if we can get one of those. So first I'll rewrite this as a one half power, so we would use power rule. So move this out front. So we get our prime of X is equal to one half tu minus five X rays to the negative one help distract off one. But we also have to apply channel. So we need to take the derivative of the insights or two minus five X. And so the derivative of two minds five extra to a zero negative. Five aces, Negative five. So this is going to give us negative 5/2 and then to the negative one power. It is going to be the reciprocal. So it would be the square root of two minus five x. So now this here is always going to be less than zero because the square root of any number should always be a positive number. Um, and then two times posit number. Still positive. And then we divide into a negative, which would be negative. So this implies that R of X is decreasing.

View More Answers From This Book

Find Another Textbook

Numerade Educator

03:27

$1 / t+1 / s=1 .$ Find $(a) d s / d r ;$ (b) $d t / d s,$ (c) Show that $(d …

01:11

Use the first and second derivatives to sketch the graph of the given equati…

01:46

Solve for $x$ in.$$\frac{1}{8^{x+1}}=16^{1-4 x}$$

02:26

Sketch on the same graph $y=f(x)=2^{x}$ and $y=g(x)=\frac{1}{2^{x}}=2^{-x} .…

01:18

Determine the equation of the inverse function.$$f(x)=\frac{11-3 x}{2 x+…

01:15

Suppose that a function satisfies the same conditions as in the previous exe…

02:15

Combine the given expression into a single logarithm.$$4[\ln x-\ln (x+1)…

03:32

A 6 foot tall man is walking towards a 24 -foot lamppost at the rate of 8 fe…

05:53

In Exercises $29-38,$ for the function determined by the given equation (a) …

01:12

If $f(x)=-3 x+9,$ find $\left(\text { a) } f^{-1}(2), \text { (b) } f^{-1}(5…