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Use the first and second derivatives to sketch the graph of the given equation. Also include the intercepts, whenever they are easily determined.$$f(x)=5+x^{2 / 3}$...

Question

Use the first and second derivatives to sketch the graph of the given equation. Also include the intercepts, whenever they are easily determined.$$f(x)=5+x^{2 / 3}$$

Use the first and second derivatives to sketch the graph of the given equation. Also include the intercepts, whenever they are easily determined. $$f(x)=5+x^{2 / 3}$$



Answers

Use the first and second derivatives to sketch the graph of the given equation. Also include the intercepts, whenever they are easily determined. $$f(x)=5+x^{2 / 3}$$

In this travel. We want to solve this function by completing the square in order to find the X intercepts. So that's read. Write this and we have three. X squared plus X is equal to a positive five. We can't have a three as a leading coefficients were not divide by the gasoline ago, but you must always be one plus X over three. It's imported five over today. Now let's user completing the score formula. We have, um, won over three over too well, that squared, which is the same thing us whenever three times. 1/2 It's quick, which is 1/6 squared, which is 1/36 or seven out of one of the 36 to both sides of the equation. We haven't X squared, plus excellent three because one of the 36 um, equals 5/3 plus one of the six. So that quadratic is gonna flak that into an X plus 1/6 squared and then our fractions. We're gonna want to have the same denominators that we're gonna multiply that first factor or first faction by 12. So five times 12 60/36 plus 136. So we have 61/36. Now, let's take the square root from both sides and we left with next was one of her. Six is equal to push in minus squatted on 61 over this one of those six statistics. Now, let's move That, um, won over six over to the other side and have an excess equal to negative 1/6 plus and minus the square. You know, 61/6. So now what we want Dio IHS. Um, write this as our X enters up. So when we haven't x intercept, we want to write this. Ask, um, a number for the X core than it and a Ciro who are or why. So this would be then want net of one of the six plus the square root of 61 over six 11 0 and then negative one of us x plus the square root of 61 number six is equal to zero, and I will be in our answers

For X intercept. Pecs equals geo. No keeping this national Tom's People Digital Find X squared plus 30 x about half minus X minus five extra ball How equal if isolating and a legal terms aside. Two X square plus 30 x to the power half equal toe X plus five extra power. Now you jindo Nespola Power is credible site so X squared plus 30 x and if you square this x squared plus five x bless x quite X so excess square in excess will cancel each other. You picked five X uh left hand site. So what party X minus five x equal toe two x five x No combining like terms 25 x quarto x Another five picks not squatting both side six. It would be five X squared Quito four X squared into five x So this is equal toe 6 25 X squared equals 20 x cubed. No dividing with pipe. You'll find 1 25 X squared equals toe four x que no. Take the stone right inside, and this is equal to jail for X Q minus 1 25 Exit squad Jiro Equality take at X squared Common poor ex minus 1 25 So find executed with Jiro on X equal 1 25 by more now verified. Answer the given question The best. Execute Jiro. Satisfy this. So execute the Jewish satisfied. So execute degenerate. A correct answer now 1 25 way for so you should check with 1 25 were poor. So this is correct. So the correct answer Execute with Jiro and 1 25

Effects. It was too minus two. It's It's quiet minus X plus three. To find out why Intercept, let's put excessive question zero. So if of Jiro is opposed to minus two, multiplied by zero square, minus zero plus three because 23 So why intercept? Yes, zero blamer today if if X is, it was too little in that guest minus two x squared minus X plus three. It was too zero on. We can write to us a squared plus x. My next easy question. You know, in fact, a form weakened by X minus one home. It'd make two weeks. Blustery is equals to zero, so either explain this one is equals to zero or two weeks. Plus is equal to zero for X equals to one on X is equal to minus three divided by toe. So it's intercepts. Odd one cor mosquito and minus three divided do Commons

Hello. Today we will be dropping a polynomial. This example gives it the function after attacks is equal to open parentheses. X minus five Post presidencies square. We want to see what this graph will approximately Looks like. Okay, let's start by, um, drying our axes like normal. Okay, So in order to make this term, um, X minus five equal to zero we know explains to be equal to positive five because five minus five equals zero. It's important to note that this term X equal cycle has even multiplicity because it's raised to an even power so that we buy the world a polynomial. We know that there will be no sign change, or there will be a found that that point it will look like either front Miley face or a frowny face to find whether, um to fund which of these shapes that will satisfy. Let's look at the end behavior as X approaches positive infinity. It will be a positive times, a positive, which tells us there would be a positive and behavior to the, um positive infinity side or to the right on. Once again, there is no sign change because of even multiplicity I'm just for the sake of accuracy it Let's find one. Um, when X is going to be equal zero. So when exposed to be equal zero, um, it's going to be negative. Five squared. So this point will be 25 okay? And this is where grapple approximately approximately look like which will be our final.


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