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The function g(T,v) = 2x* + 6ry? 3y8 150r + 10 has four stationary points_ Find aud G] classilv all of them:...

Question

The function g(T,v) = 2x* + 6ry? 3y8 150r + 10 has four stationary points_ Find aud G] classilv all of them:

The function g(T,v) = 2x* + 6ry? 3y8 150r + 10 has four stationary points_ Find aud G] classilv all of them:



Answers

Find each function value. See Examples 3 and 4.
$g(x)=x^{4}+x$
a. $g(1)$
b. $g(-2)$
c. $g(0)$
d. $g(10)$

We have G off X equal to X minus two divided by X plus four we have grossology off X is equal to zero. It implies that X minus two divided by X plus four is equal to zero. It implied that X is equal. Toto, this is the swell isn't off g off X equal to zero because at X equal to two numerator becomes zero

Let's find G of four so substitute for into the X values. So we have four square to 16 in nine times forced 36 16 plus 36 is 52 and 50 to minus two is 50 so the G of four equals 50.

No, it is considered giving functions with you. That is, if X is giving to work for fixes given to us at minus four. X plus seven. And there's another function that is G of X that is given to us as a squared plus nine X minus two. And we are just supposed to find out if minus four minus geo minus four. Okay, so now how I'm going to do that simply, I'll just find out the value of F minus four. Then I find out the value of Geo minus four, and then I'll subtract the values. So let's start by finding out of minus four so that when we found out by just shooting excess minus four in the function if isn't it so you'll get not seven like this. Now minus 14 minus $4. 16 16 plus seven nineties 23. Similar nitty of minus four will be founded by substituting excess minus four in the function G. So we'll get minus four square. Last nine times minus four minus two will get 16 minus 36 minus two, which will be equal to minus of 20. Do no coming on to this part I'll just absolutely values. The F minus four is 23 minus zero minus for Dallas minus 22. So that means what will get simply 23 plus when you do that is what the fight hence 45 is still.

So this is the problem. It gives us a function and were asked to evaluate the function in a variety of different X values. Your input but for example, of her function was G of X equals two X plus three. If we're given specific X values, your input values weaken steps A to those for Exeter function to determine its output value or its y value. So, for example, function notation. If I wanted to evaluate the function G, that means I'm going to use this function that I've been given. I could be given a specific input er x value. So let's say that input was zero. That means in my function to X plus three the x value or the input that they would like to evaluators when the input of zero. So I'm gonna replace the X value was zero and leave everything else the same. So instead of two x plus three we know have to time zero plus three because zero is the input I was given to evaluate. And then if we work out that algebra, we have to time zero, which is zero plus three, which just equals three. So therefore G of zero equals three. Looking at a different example, we have g of negative four again, we do the same thing. So we're gonna replace. We're gonna keep the two and the function. We're gonna replace this X value with the input we've been given which is negative for working that out two times negative for is negative. Eight plus three more gives us negative five. So g, the function G when the input is negative for gives us an output of negative. And we can continue this process with any input that's been given to us. So it could be a number. It could be a letter. It could be an expression. So continuing through let's look at G of negative seven. We're going to use our expression. Two time state of seven class three. Two time State of seven is negative. 14 plus three more is native. 11 so g of negative seven equals negative 11 and g of eight. We're gonna do the same thing two times eight plus three, two times eight of 16 plus three more gives us 19 nog of eight equals 19. Now again, we can evaluate these expressions with different values. So you don't necessarily have to have a number. We can also of variable or we could have some other type of expression. So let's say we had variable that wasn't X and that mutable given to us or that expression is a plus two. What this is telling us to do is to take the expression a plus two and replace it with the X value. So just like we did any other input value, we're gonna take the function to X Kloss three. And instead of the X value, I'm going to replace it with the input I've been given, which is a plus two. Now we can simplify this, but our simplification is not necessarily gonna work down to a number because I do have a variable so we can use the distributive property to simplify this expression. So two times a is to a plus, two times two is four and then we keep the plus three on again. So the expression Fergie of a plus two would equal to eight plus. So again, it doesn't look as simple. Side is the other one because it doesn't work down to a number. But we do have an expression since we plugged in an A plus to expression Parex know that this is different depending on what's in parentheses and out of parentheses. So if I was going to rearrange that idea and have G Ave but put the plus two on the outside now this is different because this is saying evaluate G of a first and then add to onto the end of it instead of replacing the X Plus two as part of the X value. So this would look different because we would plug in just a for X. So this is the two X Plus three. That's how g of a evaluates. And then at the end of that, we need to add the plus two that was given to us in the problem. So in this case, we would evaluate to a plus three, which is what g of a is. But then we have to add to to that so therefore g of A and then plus two equals the expression to a plus. So again, this is just understanding the idea that whatever the


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