Download the App!
Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.
Question
Answered step-by-step
(a) Use a graph of $ f $ to estimate the maximum and minimum values. Then find the exact values.(b) Estimate the value of $ x $ at which $ f $ increases most rapidly. Then find the exact value.
$ f(x) = \frac{x + 1}{\sqrt{x^2 + 1}} $
Video Answer
Solved by verified expert
This problem has been solved!
Try Numerade free for 7 days
Like
Report
Official textbook answer
Video by Fahad Paryani
Numerade Educator
This textbook answer is only visible when subscribed! Please subscribe to view the answer
Calculus 1 / AB
Calculus 2 / BC
Chapter 4
Applications of Differentiation
Section 3
How Derivatives Affect the Shape of a Graph
Derivatives
Differentiation
Volume
Harvey Mudd College
University of Michigan - Ann Arbor
University of Nottingham
Idaho State University
Lectures
04:35
In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.
06:14
A review is a form of evaluation, analysis, and judgment of a body of work, such as a book, movie, album, play, software application, video game, or scientific research. Reviews may be used to assess the value of a resource, or to provide a summary of the content of the resource, or to judge the importance of the resource.
04:09
(a) Use a graph of $ f $ t…
03:25
(a) Use a graph of $f$ to …
08:11
Consider the function belo…
07:21
$55-56$(a) Use a graph…
01:10
55-56$$\begin{array}{l…
01:32
(a) Use a graph to estimat…
08:14
07:17
01:04
07:23
Okay, so we're being used, asked to use the graph of after estimate a maximum and minimum value. And then we're being asked to find the exact values for these, um, stir. So I'm looking at this function. We cannot democracy that there's some sort of local max occurring right here. And we don't see any men know Ben. So there is no men, so we're going to just ignore this case, eh? So we're gonna look at the local max. So we first got to do is you can take the derivative so we first find a crime and giant crowd of X is equal to experts. One over the square root of X squared. I'm No, I'm so sorry, everybody. The derivative is one minus x over X square plus one, two to five, half power. And what we look for is Wenders to every physical zero. Because when it equals, the other is a horizontal tangent line of zero. And that's where the maximum occurred. So we set this equal to zero and one minus X equals zero. That just X is equal to one. So we know that the local max is occurring at one and it makes sense. This is it looks like a somewhere around one. And if you plug in f of won into our function, just our regular function, we get rude too. And that is the value of the maximum value. So for the then, we're being asked to estimate the value effects at which F increases most rapidly. So this is a little bit more different question. So, uh, you asked me from, Basically wears a slope essentially is the steepest. That's that's basically what we're looking for. And so this is the steepest slope occurs generally around at the inflection point because that's when the khan cavity is changing and the contract changes has usually has a steep slope current witted on the function. So yes, you have to take the second derivative. So we'LL take a double crime and after the crime has comes out to be two x squared minus three x minus one all over X, where plus one two to five power and he said this is equal to zero sent to explore minister in France. One is a quadratic function that would not necessarily have a simple factor solution. You have to apply the quadratic laments that the negative B plus or minus squared B squared minus four a. C. I'm gonna go and write that down. So you do you apply this formula and there could be touch the line in the square root of B squared minutes for a C all over two. A. And Dr Done that already and you can't X equals our three plus or minus rude seventeen. Oh, for And so what we're going to do now is we're just going to plug in both values into a prime to figure out which locals steepest. So usually this will be done on a calculator because this is that much more complicated inputs. So just come down, you get a value of negative zero point zero nine and then if you plug in three of minus, who had seventeen over before you get one point one four and one point one four is obviously bigger than negative zero point zero nine said. I mean, this is the steepest point in our function, and that is it
View More Answers From This Book
Find Another Textbook
00:29
'i really need help for this pleaseLine RU passes through two sides…
02:16
'Please help me need ASAP If the sides of a 4 X 4 square are increa…
02:26
'What’s the answer to this?Find the distance from the point (1, 5, …
01:19
'What is the median of this set of data?A.32B.36C.38D.3…
02:45
'Can somebody please help me i would really appreciate it 3.A cycli…
02:48
'PLS HELP!These line plots show the number of minutes two different…
01:11
'Can someone help me find the answer to this riddle please?an you s…
01:30
'NEED HELP WITH THIS PLEASE. NEED THE ANSWER ASAPPM is the perpendi…
00:38
'im lost again is getting harder for me ahhh im only in 7th gradeKa…
02:39
"Please help! Urgent! Will mark brainliest!Jake's band is putt…