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Question 22Let flx)-x2 -bx+2 Find coordinate of the minimum point; using derivative:(3,-71none of these answers(1,-7)...

Question

Question 22Let flx)-x2 -bx+2 Find coordinate of the minimum point; using derivative:(3,-71none of these answers(1,-7)

Question 22 Let flx)-x2 -bx+2 Find coordinate of the minimum point; using derivative: (3,-71 none of these answers (1,-7)



Answers

17-24 Sketch the graph of $f$ by hand and use your sketch to find the absolute and local maximum and minimum values of $f .$ (Use the graphs and transformations of Sections 1.2 and $1.3 . )$
$$f(x)=\frac{1}{2}(3 x-1), \quad x \leqslant 3$$

So in discussion we had to find a critical points and Andi to mind. Ah, Interval Increasing the christening of the function. So then it's true. Damn! How'd you find the f Graham off? Thanks. Now we go to minus two. Thanks. On Dan Plus ever. It wasn't a good to zero. We will have the two anxiously equal to the seven. So ex anchor juice when I'm with you so we can make a timber Rhonda be heavier now it will be. Thanks. Yeah, round thanks. Enough access. Yeah. So level seven over two is here and ah, before someone with you We can think of Leo. They say maybe one here and after seven. Allergy. We can think that, but no, that's a fine. So and we would have won and find June the epigram. You should have Ah, every murder one in saying we gonna glass Yeah, and every one of five am gonna minus So in a function we have, like, increasing here Imagine defusing. So it means that f X increased increases on the interval of romance. Infinity on the way after seven with June anywhere decrees. If you use this on interview albums, there went our Jew after infinity and the critical poems. So I have a seven on with you is no go is local maximum.

Okay, So we're asked to sketch the graph of if ah of X is equal to one minus a spirit of X and used the sketch to find any absolute and local maximum and minimum values. Okay, so I noticed that, um, the domain of F is the set of X six. That X is greater than or equal to zero because you cannot have a negative number under the radical. Thanks. So if I plug in X equals C room, I get why is equal to one like an X equals Wanna get? Why, Isaac with zero. And this has the shape of thesis kwehr root of x function. But because there's a negative in front, it's going down. Okay, so this function has an absolute maximum at the point 01 Okay, which is not a local maximum. And it has no other extreme

It's Claire's with you right here. So if C is the number in the Domaine de of a function up Can FC is the absolute max. If f of cs greater or equal to effort backs for all X and G absolute minimum if FC a smaller equal to f of X for all ex. Indeed, local maximum of FC is greater or equal to an excess. Your seat Local minimum of FC is smaller or great equal when X is in your seat. So we're gonna draw a graph below our criteria. So this is why so this is gonna be our absolute maximum. It's gonna be negative, too. One, two, three. 12 34 I six were given an equation. Off affects is equal to two minus 1/3 Ex and X is greater or equal to negative too. So we're looking at a graph in blue going to look something like this. Start here. Go, go, go, go, go! Go past six. So are absolute, Max. Uh, negative too, is equal to eight. Dirt's

Negative and rest the band and derivative of the function F of X equals x cubed minus 12 X squared or specifics that 17. So to do this, the differentiate in the usual way we bring down the power multiplied by the coefficient and then subtract one from the power what we get right Xy -24 For 36. The constant terms it appears. And then we're using the fact that the derivative is zero. Extreme point. We're going to set this equal was ever and we can see that we can divide grew back three so we get x squared minus a tech and then 4, 12 the kyocera. And so we can factories this until X -2, The next -6 and then our solutions rxc two Or x equals six. We can see this is where extreme points occur on the graph here receive that that is approximately two and six.


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