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Find the coordinates of the relative extreme point of the given function and determine the point is relative maximum point or = relative minimum point(x) =13xThe co...

Question

Find the coordinates of the relative extreme point of the given function and determine the point is relative maximum point or = relative minimum point(x) =13xThe coordinates of the relative extreme point are (Type an ordered pair. Type an exact answer )the point = relative maximum point or relative minimum point?relative minimum pointrelative maximum point

Find the coordinates of the relative extreme point of the given function and determine the point is relative maximum point or = relative minimum point (x) = 13x The coordinates of the relative extreme point are (Type an ordered pair. Type an exact answer ) the point = relative maximum point or relative minimum point? relative minimum point relative maximum point



Answers

Find the coordinates of each relative extreme point of the given function, and determine if the point is a relative maximum point or a relative minimum point. $$f(x)=e^{-x}+3 x$$

In discussion. Where you calling abound They with the under age of the X, we get equal Thio the each of the Ex Im. So when the evil eye eager to be listen even only if I must because of the and I'm gonna be in this question were given the function f X, they go to the five x minus to give to the X, and we need to find a relative extreme er so the first time we need to find a derivative on the function. Then they drift in the five x a culture of five. The riveting reason which stays the same thing. And we need to find a critical point, you know, to that we need to sell it. Any coaches their own doesn't implies that which Uganda, each of the X pickle to the five over to and then just in this property here doesn't realize that X must equal to Ellen under five are with you. So we found a critical point now and the next time we will make a table to use the first derivative test here from this infinity to infinity when the 11 5 hour to here don't have the employment of X and now have this? Yeah. And then on the 51 with you, it will be smaller than one. So Buddha one here on the right there on the left here and we would go into the F prime. We had a feminist equal to positive. Doesn't be negative here. And then the function here, we're going up. Then it's going down. So curly from here we see. Do you have a relative maximum here? And it means that the relative maximum it goes to the point. Atlanta five hours to on a function here will be the five times and then the five on with U minus to eat to the 11 of five armed with you. It was simply fighters and got the Atlanta five on with you, then 505 over to minus five. And this will be the red early to maximum here. But we have no relative minimum

So we're given the function. Why is equal to X square LA gigs domain being x greater than zero. We need to find the relative extreme points that is appointed waste. The first already goes to zero. Then we need to find the second derivative check if their relative points their points of Maxima or MINIMA. So let's just calculate the first derivative using the product proof setting the very the X zero, we get XKR vehicle zeros in the domain that's greater than zero. So we get to Law X plus one equals zero. Log X is equal to minus one by two. So accessible do it is the power minus one way to and why is equal to X squared log X So at this point, why is equal Do is equal. Do you've power minus one in two minus one by two. So minus one way we So the coordinates off the extreme points that it is part minus in May 2 comma minus one way. Do we unless calculate the second derivative. So first derivative is X times too long, Express one. Yeah, So we use a product tool. Okay? Yeah, they called too long eggs plus three. No, we secure, like physical do. It is about medicine. Very to is equal to which is greater than zero. So? So the relative point extreme point is a point off minimum.

Alright for this problem, we want to find all points X. Y. Where f x Y has a possible relative maximum or minimum, F of x, Y equals X cubed plus x squared y minus Y. So we just want to find when both partial derivatives of F equals zero. So partial X F is going to be three, X squared plus two, X Y equals zero, partial Y F is going to equal, then that's x squared minus one equals zero. Which means we'll have X squared equals one, X equals plus or -1. Then We can substitute that in up here. If we have X if we take first x equals one and that means we'll have three plus two, Y equals zero, Which means that we'll have why is going to equal negative 3/2? And then if we have that x equals negative one, we'll have three minus two. Y equals zero, Or y equals 3/2. So our solutions are going to be a positive one, -3/2 negative one. Positive 3/2.

For this problem, we are asked to find all points X Y where f of x Y equals x squared minus Y cube plus five X plus 12 Y plus one as a possible relative maximum or minimum. Which means we want to solve for when the partial derivatives with respect to X and Y equals zero, partial with respect to X. It's going to be two, X plus five equals zero. So that means we're looking for X equals negative 5/2. And the partial with respect to why it's going to be negative three, Y squared plus 12 equals zero. Which means that we are going to be looking for. Well, we can divide everything through by three. So we'll have when or divide everything through by three and then shift the Y squared over to the other side. So we'll be looking for where Y squared is going to equal four, Which means that we are looking for y equals plus or -2. So our candidates are negative 5/2 positive too, and negative 5/2 negative two.


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