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zloy xaker [14]
2 years ago
11

Find the value of x for which the function y = x5-x³ + x² - 1 has a local minimum.

Mathematics
1 answer:
melisa1 [442]2 years ago
7 0

The given function presents a local minimum in the coordinates (0,-1).

<h3>Factoring</h3>

In math, factoring or factorization is used to write an algebraic expression in factors. There are some rules for factorization.  One of them is a factor out a common term for example: x²-x= x(x-1), where x is a common term.

For solving this question, the given equation should be rewritten  from the factoring.

x^5-x^3+x^2-1=\left(x+1\right)^2\left(x-1\right)\left(x^2-x+1\right)=0. Then, you have 3 equations.

From the Zero Factor Principle, you can write

Equation 1

(x+1)²=0

x+1=0

x= -1

Equation 2

x-1=0

x=1

Equation 3

x²-x+1=0

x_{1,\:2}=\frac{-\left(-1\right)\pm \sqrt{\left(-1\right)^2-4\cdot \:1\cdot \:1}}{2\cdot \:1}\\ \\ x_{1,\:2}=\frac{-\left(-1\right)\pm \sqrt{3}i}{2\cdot \:1}

From these points it is possible to plot a graph and you can see that the local minimum presents the coordinates (0,-1).

Read more about the factoring here:

brainly.com/question/11579257

#SPJ1

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Evgesh-ka [11]
D because you need to make the denominators have a common multiple.
5 0
2 years ago
P is the midpoint of ad aq:qb=2:3 show that pq is parallel to cb
sveticcg [70]

Answer:

question a) is 2q+3p

Step-by-step explanation:

4 0
3 years ago
Gina wants to go to the water park with her friends. They have a total of www dollars to buy 555 tickets. Each ticket costs 1515
alexdok [17]

Answer:

151,515 * 555 = www

Step-by-step explanation:

Yeah so basically www is the total amount of dollars they have to buy 555 tickets. And each ticket costs $151,515, so like it's the cost per ticket times the amount of tickets to get the total amount of dollars

7 0
2 years ago
A land owner is planning to build a fenced-in, rectangular patio behind his garage, using his garage as one of the "walls." He
Vitek1552 [10]

Answer:

Maximum area = 800 square feet.

Step-by-step explanation:

In the figure attached,

Rectangle is showing width = x ft and the side towards garage is not to be fenced.

Length of the fence has been given as 80 ft.

Therefore, length of the fence = Sum of all three sides of the rectangle to be fenced

80 = x + x + y

80 = 2x + y

y = (80 - 2x)

Now area of the rectangle A = xy

Or function that represents the area of the rectangle is,

A(x) = x(80 - 2x)

A(x) = 80x - 2x²

To find the maximum area we will take the derivative of the function with respect to x and equate it to zero.

A'(x)=\frac{d}{dx}(80x-2x^{2})

             = 80 - 4x

A'(x) = 80 - 4x = 0

4x = 80

x = \frac{80}{4}

x = 20

Therefore, for x = 20 ft area of the rectangular patio will be maximum.

A(20) = 80×(20) - 2×(20)²

         = 1600 - 800

         = 800 square feet

Maximum area of the patio is 800 square feet.

7 0
3 years ago
John ran the​ 100-m dash with a time of 9.96 sec. If this pace could be maintained for an entire 26-mi ​marathon, what would his
soldi70 [24.7K]
We know that 
1 mile----------------> 1609.34 meters
26 miles---------------> X
X=26*1609.34=41842.84 m

I apply a rule of three to know the time

if 100 m---------------9.96 sec
41842.84 m----------> x
x=41842.84*9.96/100=4167.5468 sec

to get minutes I divide it by 60---------> 4167.5468/60=69.459113 minutes

to get hours I divide it by 60----------> 69.459113/60=1.1576518 hours

1.1576518= 1 hour 9 minutes 27.55 sec

the answer is 1 hour 9 minutes 27.55 sec------->(4167.5468 sec)

3 0
3 years ago
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