let-fxx-e2-x-a-find-the-values-of-x-for-which-the-slope-of-the-curve-yfx-is-0-b-explain-the-meaning-

Question

Let $f(x)=x e^{2 x}$
a. Find the values of $x$ for which the slope of the curve $y=f(x)$ is 0
b. Explain the meaning of your answer to part (a) in terms of the graph of $f$

Shumayal N · Accepted Answer

okay, So because we have two functions that are multiplying with each other in order to be active in derivative, we need to use the product rule, which states that first, to keep the first term constant and take the derivative of the second term into the power to X, which is each of the power to extend to plus. Then you keep the second term constant and take the derivative of the first term. Next, we can simplify this by taking D to the Part two X. There&#x27;s a common factor on your love toy this two x plus one inside the parentheses. In order to get the point at which the ingredient is zero, we set the derivative equal to zero. So has your legal two X plus one. Thereby X is equal to minus half For the second part. Let&#x27;s find the value of why when X is equal to minus absolutely substitutes. Why into our equation X to the power to eggs. So we&#x27;ll have minus half E to the policy to Linz minus half. Then this gives us marinas wouldn&#x27;t over to you. So basically what this means is that at the point minus half on minus one over to e be tangent is horizontal, where the Grady Int zero

Thomas Pauly · Answer

So we&#x27;re giving this function f of X. We want to find the X values such that the slope of the tension line at those X values. Zero. Let&#x27;s first find the derivative of this function. If prime of eggs, we have a function of X multiplied by a function of X. So if used product rule first function derivative of X is just one. Then I multiplied by the second function and plus leave the first function multiplied by the dribble of the second, which is times to eat. The two x Just bringing down there, too, simplifying us a little bit. This gives us eat the two x plus two x into the two X. We actually want to set this 20 So that&#x27;s self Rex. So you know, do this. Let&#x27;s subtract one of these over. We get negative. E two acts is equal to two X each of the two acts. We have a common term each of the two X on both sides. You could drop those and just get negative. One is equal to two acts. So for X defied by two on both sides, I think it&#x27;s this negative one half Ziegel Dax. So X equals negative. One half the slope of the tender line is equal to zero. And what this means with respect to the function, Here&#x27;s a function of X here. The red line right here is our point. Negative one half. You know that this is a minimum in the graph. And so at this point, the slope of the tender line is zero.

Peter Winans · Answer

all right with this question we&#x27;re examining, he spies function where X is equal. The acts Yeah, excess listeners equals zero. It&#x27;s people X plus one X is greater than zero. So if we do a quick sketch in an idea what this curve looks like and when X is less than or equal to zero, why is equal that acts? So that&#x27;s just going to be a line the slope of one. Why receptive? Zero. And when exes less than zero or when X is equal zero. So right here, we&#x27;re gonna have a point. That&#x27;s part of the solution. Said That&#x27;s part of domain for that part of the function. We&#x27;re never lying the best. Like that&#x27;s what something like that. No, if X is greater than zero. F is equal X plus one. So this interval starts at zero. But we&#x27;re not including zero in this part of the ground. So it&#x27;s got to get open circle right there. So we have a graph. Those something kind of like that. They&#x27;re peaceful, its function with this gap in the middle. As I approach zero from the right, I repudiated prevail, use when I&#x27;m approaching zero from the left. So the next thing we want to talk about that is what the derivative looks like went into the left zero vs one. Until the rate of zero so X is less than zero, the limit derivative will be equal to go on that his age is approaching zero. Well, the function his acts. So this is just gonna be X plus a H minus X over h. So this will be the limit. It&#x27;s Each is approaching zero x minus X will be zero. So we&#x27;re gonna have over each is going to be down here. Limit one. His age is approaching zero. She&#x27;s going to be one. So again, it&#x27;s a nice line. Should have a constant slope. In this case, the slope is going to be one went on to the right of one X is greater than one that is equal to X plus one so crying well in that as each is approaching zero with X plus a h one minus X plus one all over age. So the next thing we have to do now minor league terms we will limit is a cheap approaching zero to be left with each over age which is the limit is each approaching 01 which is also going to be one. So we see that are derivative is one both on the left side, on the right side of zero. So if we were to draw a graph that demonstrated a private backs on our graph the prime of axe no circle to the left with one it&#x27;s equal to one to the right of arms are to the left zero its people the one. So the rate of zero, it&#x27;s equal the one. But yeah, is not defensible. Yeah, X people zero because it is discontinuous. Yeah, X equals zero. Because again, if you go back to your original graph, we have this. Yep. Here. Okay, I&#x27;m approaching one from the right from approaching zero from the left. We have this Gabri here, which means it&#x27;s not continuous. And if the functions that continuos that it&#x27;s not gonna be differential so that our recession that he&#x27;s vice function

Ankit Gupta · Answer

we have been given the graph off. Why is equal to FX and using this graph, we have to find the truffles. Why is a quarto fof two X minus one and in five B, we have to find bicycle do two times F one by two x So impact a first, let us find f off two X So since two is greater than what their full in step number one, we will shrink ethics horizontally by effected ALS one by two to get f off two X and step number two, we have to factor in this minus one shift. So now we have obtained f off two weeks. So we will shift f off two x one units downwards to get f Wolf do X minus one now in five. Number B first developed in F or one bite weeks now clearly won by two is less than one. Therefore, then step number one even stretch ethics by effected off do horizontally to get Air Force one by two X and step number two. We have toe factor in this my application by two now, since two is greater than one and we have complained two times f off one by two x So level stretch the often bicycle toe one by two and f off one by Twix Vertically by effected off Do DOn&#x27;t get two times F off one by two x

Ankit Gupta · Answer

So in this question, we have to find the raffle. Why is it where do FX minus one and why is equal to air four X minus two from the given graph by is equal to ethics. So we know that you d that when we have to shift along the positive by axis. Suppose we&#x27;re shifting the graph off Isaac Quinto FX les de units along the Y axis. So the resulting graph will be ethics Les Bee. It is negative. Deep shift along the Via access The graph will be FX minus t. Similarly, when the shift is along the X axis surfers, it is past the units. The graph will be why is it called F X minus D? And if it isn&#x27;t in minus T units graphically bicycle FX plus be so for the graph of Y is equal to FX minus one. We even have to shift minus one units candy by excess direction that this one unit along being negative by access for bicycle toe FX minus two. We will use this property so therefore we will have to shift bless two units in the less access direction which is the right direction

Rakesh Kumar Sharma · Answer

indiscretion first, See how to make the off at full face. And you know, Shrek suspends the next meet its truffles. So this is really my exes. This should be on expenses. Okay, So I&#x27;ll give you something like that. And you think Dennis, in this stuff that the value if I take this point, that&#x27;s it. So this part remind Missy, and if you see when I lose approximately the scene, Okay, Well, Lucy imagery that f every week was so therefore my mistake. Okay? Because why f off complexity was extra spare. Is there even function? So the value of the function and efforts be because for myself, minus e, we can also right, because it&#x27;s a union from so therefore, actually, people, so four minus X and even kill Easy, slow. The lion does this, ladies and see for general line the slow off border line is you okay? And even, let&#x27;s say slow for the human point to the small, Really? It was to finally went my decision point. So that point given causes a f it and minus a comma at fault minus e. Okay, the snowfield defining point. My destination point. So that will be efforts minus it. Marinas F off it, divided by minus eighth dynasty. Okay. And so this we can you see that? A single share for Martin receipts ofl my civic. And I did not miss and fall. Yeah, okay. And f off a as it is doing. I didn&#x27;t write this a minus these real cans along. So the Soviet Premier This issue for the Slovene zero in the questionnaire also asked for the slow but excuse to Are you okay? So accessible severe? You see the danger the engine isn&#x27;t either. Accepts is okay. If this is the pain excesses that ended in this, then give slow will be geo egg exoduses years. Okay, that is

Problem

86-89. Second derivatives Find $\frac{d^{2} y}{d …

Problem 85 Hard Difficulty

Let $f(x)=x e^{2 x}$
a. Find the values of $x$ for which the slope of the curve $y=f(x)$ is 0
b. Explain the meaning of your answer to part (a) in terms of the graph of $f$

Answer

a. $x=-\frac{1}{2} \quad$ b. The line tangent to the graph of $f(x)$ at $x=-\frac{1}{2}$ is horizontal.

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a. $x=-\frac{1}{2} \quad$ b. The line tangent to the graph of $f(x)$ at $x=-\frac{1}{2}$ is horizontal.

Calculus Early Transcendentals

Catherine R.

Kayleah T.

Kristen K.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

William Briggs, Lyle Cochran, Bernard GilletCalculus Early Transcendentals

Catherine R.

Kayleah T.

Kristen K.

Michael J.

William Briggs, Lyle Cochran, Bernard Gillet

Calculus Early Transcendentals