if-h2-4-and-h2-3-find-frac-ddx-left-frac-hxx-right-mid-x-2

Question

If $ h(2) = 4 $ and $ h'(2) = - 3, $ find

$ \frac {d}{dx} \left( \frac {h(x)}{x} \right) \mid x = 2 $

Frank Lin · Accepted Answer

So So the derivative of that. You mean computed by the caution room, which gives you this on DH times X minus edge X times that they&#x27;re with you off, actually. Is what? So you probably actually forced to do so this woman you evaluate had actually close to two. This will give you as a private to Jewish problem too. Might essential to over two square, which is, for that&#x27;s problem to its negative three. So this step six special too, is Force No minus four over for so minus. Nephew. Tenable for ninety five over two.

Ankit Gupta · Answer

were given a polynomial function. That is it. Your fix is equal Toe X plus two multiplied with X minus four whole cubed now, First of all, we need to find the X intercept for the given function, so they will be at minus two and four repeated trays at four. Since the multiplicity is three off the real solution four. Now we need to find the function first, advise equal do etch Off X minus two. So then they given function will change Toe X minus two plus two multiplied with X minus two minus four. Whole cube, which will become X since minus two plus two will get cancelled, multiplied with X minus six Whole cube. So the new X intercept will now be at zero on six.

Nez Nikoo · Answer

Okay. Use equation. They&#x27;re telling us to find each of exit H of X is minus slow. So I put a minus 12 year and you see right away I can cancel this three this file submit. This becomes four. So now the equation is X minus four. Swear pickle. Two months. Yes. Okay, so now get a square root of each side. Get X minus four is speak well to plus minus and minus one becomes I four becomes 22 becomes too. I right and X is equal to four plus minus two I with many of these very straightforward. But when you have to know is if I have minus four, I really have a minus one and it four. And if you get a square root of this, what happens? You have I It&#x27;s a sign and four becomes too. So this is saying is to I think a little extra explanation again, but check. Thank you.

Ankit Gupta · Answer

According to the question we have HR picks equals three months, led by X minus four whole square. Now we have to find all valuable fix for Bt H affects equals minus 12. Now what we will do is we will simply value three multiplied by X minus four holes where equals minus acquitted. So three multiplied by X minus school. Whole square will become minds up 12. But when we divide both sides of the quality by three, we will have X minus four post where equals minds of food now carefully observed that in the left hand side we have a positive quantity, whereas in the right hand side, we have a negative quantity. So from here we can as you that our solution is going to be a complex number because there is no real numbers for reach. This question is going to be satisfied. So let&#x27;s blue square root in both sides of the quality. So we will have X minus four equals square root of minus afford Now X minus four equals start of mine. So four can breathe in and started a full multiplied by a spirit of minus off one. And we know that iota is nothing but squared minus off one they&#x27;re corrects minus four will become. I made a small a small mistake when we removed the square. We will get a plus minus before, so that&#x27;s it. So we will have less minus science. So now x minus score will be compressed mind so spare. The four is number two and spirit of minus minus one is fired up. So we&#x27;re getting two different questions. And there it&#x27;s minus four equals who iota on X minus four equals minds of who iota. Now my next minus 40 coast Wilder than X will become full Let&#x27;s do iota and when X minus four equals minds off Wilder when we will have X equals four miners off who iota So we&#x27;re getting through different solutions on there. X equals four. Placed y order on X equals four minus of who iota. So this will be our final required answer

Robert Leedy · Answer

unplug Negative three into F bursts. So that gives us two silently. Rewrite that. Two times negative. Three plus four 12 times negative. Three is negative. Six at four. We get negative to there. Now we&#x27;re gonna plug negative to into H. Thank you mind that was at that negative three. So now we&#x27;re employing negative two, and h, that just is negative. Two squared, Which is he? Go four.

Charles Carter · Answer

that this problem wants me to find capital age of negative too. And press to do that. We&#x27;re just gonna replace all of our X values with pregnancies. And in those pregnancies, we&#x27;re gonna put negative Teoh. Okay, Simplifying is gonna give us negative squared, which is poor. We subtract a negative to. We&#x27;re gonna be adding Teoh. So capital h of negative two would be equal to six. Thank you very much.

Frank Lin · Answer

it&#x27;s Claire&#x27;s. So when you read here so if you&#x27;re gonna use a closure, we have D over DX. Each of nuts over x X is equal to this is equal to the derivative of H times X minus H of X times one all over X Square for X is equal to two in their h, the derivative of two times two minus age of two times one all over two square, just equal to negative. Three times two minus four times one. We&#x27;re just plugging in the values that we got, then we get negative £5.

Problem

If $ g(x) = xf(x), $ where $ f(3) = 4 $ and $ f'(…

Problem 46 Easy Difficulty

If $ h(2) = 4 $ and $ h'(2) = - 3, $ find

$ \frac {d}{dx} \left( \frac {h(x)}{x} \right) \mid x = 2 $

Answer

$-5 / 2$

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