solve-the-given-problems-find-the-linearization-of-the-function-fxfrac6-e4-x2-x3-for-a0-2

Question

Solve the given problems.
Find the linearization of the function $f(x)=\frac{6 e^{4 x}}{2 x+3}$ for $a=0$.

Edward Downes · Accepted Answer

Okay here we get given a function. That function is F of X equals six. Either the four X over two X plus three. We want the linear ization of this function at a equals zero. So for linear ization we need two things. We need this point and a slope. We&#x27;ll start off with the point the X coordinate. The point is given to us zero. We need to find the like coordinate. So we&#x27;re going to compute F of zero. Just six ft of the zero of the zero plus three. Should give us 6/3. Just to coordinate is zero comma. Two will hold on to that later. Okay, now we need the slope so we need the derivative for that. So after kind of X. This will be another closer role. We&#x27;ll set up on the division symbol, the denominator times the derivative of the numerator. There is the numerator will be 24. Either the four X minus the numerator times the derivative of the denominator all over the denominator square. Okay. We could spend time simplifying this but we don&#x27;t really need to we just need to evaluate this at our A value so we evaluate it at a equals zero. Okay, I&#x27;ll skip some of the calculations here. So give us three times 24 ft of the zero minus six times E. To the zero times two. All over two times 00 plus three. It&#x27;s three squared mm. Little bit more simplification here. 24 times three. We&#x27;ll have 72 minus 12/9. Should give us 60 of the nine which will simplify to 20/3. Okay. And this is our slope. So how do we put the linear ization together? We use point slope form I minus Y. One equals M. It&#x27;s x minus X. One. We&#x27;ve got to point up the top and a slope that we&#x27;ve just found substitute these in quick little bit of rearranging can get us to the answer. We&#x27;ll see in the back of the book, which is why you cause 20/3 X plus two. Just move into two over and distributing the 20/3. And that&#x27;s it.

Amrita Bhasin · Answer

Okay, We know L A box is half of a post up prime of eight times X minus a. They&#x27;re for UVA is negative. Eight, that is, four plus three equals negative. Nine. A primal X is three x squared, minus two acts. They&#x27;re for a problem. Negative to plugging that in three times. Four months, two times negative to a 16. Therefore, L A box is negative. Nine was 16 times exposed to. Therefore, this simplifies to 16 acts close 23.

Jack Chen · Answer

all right. Essentially the immunizations. Just the dungeon line. So we just refers tech illiterate tive. So we have by the power we have for X cubed six x So the curative, um, at X equals two minus one will be if prime off minus one, it&#x27;s given by minus 10. So the 10 John my is given by wide minus F one because to the curative, which is a slope. So it&#x27;s minus what Times express one. So plugging off this information we have why he closed the A minus 10 x minus six, which is the memorization.

Doruk Isik · Answer

in this problem Where us? To find the lean years they showed up The function rac warrant. Uh, 16. So let&#x27;s start with finding David. You&#x27;re a primal backs from this is, um you were four extra native. What board and what&#x27;s it like to function on their wits about at a given point of 16 is eight and F current 16 is for your egg. So the musician Opa have this F 16 plus eight prime 16 times X minus 16. So now we people look thanks and your eight 16 prime ships seen be finally musician to be three accelerate plus two

Jack Chen · Answer

So in this question, we want to find out of miniaturization a taxi cost way, which is just attention line. So by the slump point form for attention line. We have to figure out these three information. So the sooner point from give is given by White minus a full face because toe prime of eight, which is a motive and it&#x27;s a stroke off attention line Times X minus eight So a is given a 16. So we need to figure out what safe off a and they&#x27;ve profit. So if a way equals two f off off 16 which is, um, 16 23 over full, I&#x27;m so be careful about this. It&#x27;s actually close to 16 to the 1/4 ended to the three. So you inside the break it and we have just two so immune evaporate en route for duty. If we need to figure out the curative off first, I love power or it&#x27;s given by three or four extreme minus 1/4, and we plug in X equals 2 16 So we have 3/4, um, comes one over 16 to the one number fault. So we just given by 3/8 With this information, we have wide miners hit because 23 or rate times X service 16 Some of this mind state to the other side we have Why? Because toe through over eight ex miners the second Article six in the process which is through your rate takes pass to so the immunization is given by this through over eight express to

Robert Daugherty · Answer

so section 3.9 Problem number one here. We&#x27;re dealing with approximations We can get from a derivative. So in this topic, we talked about the linear ization. So an approximate linear function to a curve at a particular neighborhood. So near where we took a derivative. So what is it approximately notarization? Your point. So the linear ization of a function is going to be if we start with function F so it&#x27;s gonna be f of a plus f prime of a times X minus A. So we&#x27;re given a function here f of X, and it&#x27;s a polynomial x cubed minus two x plus three and were asked to find the linear ization. What is that Approximate linear function near a equal to Okay, so in this case, what we&#x27;re going to need or in any effort to and f prime of two. So first of all, let&#x27;s just figure out. So if we figure out what, um f of to ISS so f of two is going to be, what, eight minus four plus three. That&#x27;s four plus three, which is seven. And then when you look at F Prime of X is going to be three X squared, minus two. So f prime of two is going to be three times four minus two, which is 10. So the linear ization we&#x27;re gonna have the linear ization function is going to be f of A, which is seven plus f prime, which is 10 times X minus two. So what this comes out to be is what, 10 X minus 20 plus seven. So that is what 10 X minus 13. So that is the linear ization. So near and the point a equal to this linear function is a decent approximation off our function near that point. So near the point, a quick to that is our approximate linear function.

Problem

Solve the given problems. Use a calculator to dis…

Problem 40 Easy Difficulty

Solve the given problems.
Find the linearization of the function $f(x)=\frac{6 e^{4 x}}{2 x+3}$ for $a=0$.

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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Precalculus Review - Intro

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Basic Technical Mathematics with Calculus

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Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus