5

Zx _ 5 for x < 3 Sketch flx) where f(x) = {(x _ 3)2 + 1 for x > 3...

Question

Zx _ 5 for x < 3 Sketch flx) where f(x) = {(x _ 3)2 + 1 for x > 3

Zx _ 5 for x < 3 Sketch flx) where f(x) = {(x _ 3)2 + 1 for x > 3



Answers

Sketch the graph of a function that has the properties described.
$f(3)=5 ; f^{\prime}(x)>0$ for $x<3, f^{\prime}(3)=0$ and $f^{\prime}(x)>0 \text { for } x > 3.$

Mhm. Hello? So here we have, the graph of F x is equal to x cubed minus five X squared is going to have the general shape of X cubed. Where as we head off to the left we're down to the left and up to the right we have that our um X intercept and y intercept is at the origin. Um And we have our two zeros here at 00 and then our other zero is at five. Um And um yeah and here we have again the graph of F X is equal to X cubed minus five X squared here graft and decimals.

For this problem, we are asked to sketch the graph of the function F of x equals two minus x squared for x between one and three and two minus three X for x between three and five. Then we must locate the absolute extreme of the function over the given into. So we know that we have something and I'm just going to be doing a very rough sketch not to scale, you know that we have something that goes down parabolic lee. And then we can note that at that switching point of the definitions, we will switch the definition smoothly because we have 2 -9 and then to -9 on either side. Then after going or descending parabolic lee, we have something that goes out linearly, but we can see that this is consistently decreasing over the entire interval. So we can see then that our maximum is going to be at the point f of one, which will be 2 -1, which will just be one. And our minimum is going to be at the point f of five, Which will be to -15, which would be negative 13.

Solution for the given question, but it's all the given question solution. Remember, question questions like this. They have human. The given question is the cubic equation on. Also, they said, make it if if X is equal to zero. So if make it physical zero find out the X value. Find out the X value which are really we have so pubic question. Generally, three x one will be there to find out Really values here X is equal to one minus one to minus two. You can absolutely ministry like that. You can subset even zero so you can substitute whenever we suffered that value. If you get the family and zero, that is the rial X value for the FF IX. So X is equal to one. I'll take substitute excuse mints one cube, minus one square, minus three tomorrow one plus streets absorbing one in the place of things. When did you mean to one again? Minus one square. Also one minus three plus three Here, minus one plus one will get canceled. So your personal embarrassment also passed three months. Three year cancer. The answer is you so existing call to understand how physical the honesty. So it satisfies. X is equal to one here. X is equal to one satisfies this is the real answer. Now we'll check like that a tool so we can check if finance of God zero That is the real value of physical tools so we can check to checking mix to you. Look at the question Ex Cubans excess square in the play. Six we have substitute to so Tokyo minus two X squared minus Strange took place Crazy quantum to cable to those four photos 88 minus four minus six plus three He really get it as eight minutes for its four minus six months plus three ministry So one hears zero We didn't get so excess recall toe Norota solution for death effects. Similarly, we can check even minus one. Also, you can check minus one minus two. Also I'm taking minus one minus one whole cube minus off minus the whole square minus three off minus one plus three And I'm checking minus one in the face of fixing the question. So minus one whole cubicle as minus one minus one holds where it's plus one into minus minus one plus three plus three we'll get s O minus to plus six will get here. So for this is also not isolation financially should get zero. Similarly, we can check minus two also can take X is equal to minus two. So minus two whole cube minus off minus two. Whole square minus three off minus to plus three. The question. I'm subsiding. X values minus two minus two Ball. Cuba's minus eight minus two squares for minus four plus six plus three. How much you'll get minus, uh, eight. Minus four is minus 12 minus nine. Minus three will get So this is also not answer. So the answer is X physical toe. One Minister Solution X is equal to one.

After that in this question were given a function. FX is equals two X cubed minus three X square minus nine explodes 27. I told to find values off eggs that would make dysfunction greater less than zero. So to find these values, we have to find the value of exile. Make the function equals to zero. To solve this equation, we have two factories it on To find the other factors, we have to divide it by one of the factors. So I guess one of the factors off this expression is gonna be X minus three. So let's divide X goes here X square, X squared times minus three minus three X square. Remember nine exposed 27 eggs goes into minus nine. Eggs minus 99 times exist nine nine times trees, 27 days Minda. So this is gonna be the second pacto, and it could be simplified into eggs equals through close on minus three. So now we can right answer. If X is greater than zero. If X is greater than three. If X is less than zero, Youth X is less than minus three. Or the models of eggs is less than three. This is gonna be the answer, and we're also told to sketch a graph of dysfunction. I've gone ahead and used a graphing calculator to sketch a graph, and it looks like this. So the graph of X Q. My nose three eggs square minus nine eggs goes 27 No.


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