graph h(x)=x^4-3x^2+x. identity the x intercepts and the points where the local maximum and local minimum occur. determine the intervals for which the function is increasing or decreasing.Round to the nearest hundredth if necessary
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I hope this helps you. Give a like
The x-intercept are x = 0, x = -1.9, x = 0.35, and x = 1.5.
The local minimum is 1.
The function is increasing at the interval (-1.5, 0.5) and (1, ∞).
The function is decreasing at the interval (∞, -1) and (0, 1.5).
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
h(x) = [tex]x^4[/tex] - 3x² + x
The x-intercept is when h(x) = 0.
0 = [tex]x^4[/tex] - 3x² + x
From the graph, we see that,
The x-intercept are at x = 0, x = -1.9, x = 0.35, and x = 1.5
Now,
h(x) = [tex]x^4[/tex] - 3x² + x
h'(x) = 4x³ - 6x
h''(x) = 12x² - 6 (positive)
So,
h(x) has a minimum value.
h'(x) = 0
4x³ - 6x = 0
4x³ = 6x
4x² = 6
x² = 6/4
x² = 3/2
x² = 1.5
x = ±√1.5
x = ±1.22
The minimum values are:
h(1.22) = [tex]x^4[/tex] - 3x² + x = -1
h(-1.22) = [tex]x^4[/tex] - 3x² + x = 1
The local minimum is 1.
From the graph, we see that,
The function is increasing at the interval (-1.5, 0.5) and (1, ∞).
The function is decreasing at the interval (∞, -1) and (0, 1.5).
Thus,
The x-intercept are x = 0, x = -1.9, x = 0.35, and x = 1.5.
The local minimum is 1.
Increasing intervals are (-1.5, 0.5) and (1, ∞).
Decreasing intervals are (∞, -1) and (0, 1.5).
Learn more about functions here:
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you need to do it step by step and use something that will help
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4x + 3 = -9 slove the equation
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Answer:
x = -3Step-by-step explanation:
4x + 3 = -9=> 4x = -9 - 3=> 4x = -12=> x = -3Conclusion:
Therefore, x = -3
Hoped this helped.
[tex]GeniusUser[/tex]
can someone help me with this problem!
__ + (4) = -1
whats the missing number
( I swear I'm smart lol)
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Ignore this this is just for 20 words
There are 900 seats on a train. 540 of the seats are empty. What percentage of the seats on the train are empty?
Answers
60% of the seats on the train are empty
you have to divide 900 by 9 to get 100 because percents are out of 100, then you have to divide 540 by 9 also.
Answer:
60%
Step-by-step explanation:
Because there are 540 empty, and 900 total, you need to divide 540 by 900.
540/900=54/90=6/10=60/100
When you get 60/100, or 0.6, you know that it is 60 percent because percent is out of 100.
Choose the best response to the question below:
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Answer:
d
Step-by-step explanation:
the answer is d because 2×3 equal 6
[tex]\\ \sf\Rrightarrow a*b=ab^2[/tex]
a=2b=3[tex]\\ \sf\Rrightarrow 2*3[/tex]
[tex]\\ \sf\Rrightarrow 2(3)^2[/tex]
[tex]\\ \sf\Rrightarrow 2(9)[/tex]
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En un barrio de 3.120 habitantes, se realizó una encuesta a 620 sobre la preferencia
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probablemente en el barrio, ¿cuántas personas prefieren lo mismo?
Answers
Es probable que el número de personas a las que si les gusta comer huevo al desayuno todos los días sea 90 personas.
Según principios estadísticos, es posible determinar una tendencia general utilizando una muestra de la población. En otras palabras, es posible tener una idea aproximada de las preferencias de una población si se logran determinar las preferencias de un pequeño grupo de dicha población.
En este caso sabemos que la población total equivale a 3120 habitantes, la muestra equivale a 620 personas y en la muestra 18 personas comen huevo al desayuno todos los días.
Usando una regla de tres podemos determinar la tendencia general:
Si a 18 personas de 620 les gusta comer huevo todos los días al desayuno, a cuántas personas de 3120 les gusta lo mismo.18 = 620x = 3120x = 18 x 3120 / 620x = 56160 / 620x= 90Es decir que aproximadamente 90 personas tienen esta misma preferencia.
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Answer:
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Step-by-step explanation:
Have a nice day :)
Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
solve the following equation
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Hi,
x² + 8x + 12 = 0
a= 1 ; b= 8 c= 12
∆ = b² - 4ac
∆ = 8² - 4*1*12
∆ = 64 - 4*12
∆ = 64 - 48
∆ = 16
∆>0 :
x1 = (-b-√∆)/2a = (-8-4)/2 = -12/2 = -6
x2 = (-b+√∆)/2a = (-8+4)/2 = -4/2 = -2
S= { -6 ; -2 }
x = -6
or x = -2
✅(•‿•)
Answer:
x = -6 x = -2Step-by-step explanation:
x² + 8x + 12 = 0
➺ x² + 2x + 6x = 0
➺ x(x + 2) + 6(x + 2) =0
➺ (x + 6)(x + 2) = 0
Whether, x + 6 = 0
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⠀⠀or,⠀⠀⠀⠀ x + 2 = 0
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Answer:
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Answer:
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Step-by-step explanation:
you can replace the decimal pint with an and so that its
eight thousand twenty four and sixty two hundreths
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Step-by-step explanation:
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Answers
Answer: There are no solutions
Answer:
Two
Step-by-step explanation:
x^2 = 4x - 5 is equivalent to x^2 - 4x + 5 = 0 in standard quadratic form.
All quadratics have exactly two roots/solutions.
In this case the coefficients of the polynomial are 1, -4 and 5, and so the discriminant is b^2 - 4ac, or (-4)^2 - 4(1)(5), or 16 - 20 = -4.
Since the discriminant is negative, we conclude that this polynomial has two complex roots/solutions.
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Answers
Answer:
2/1=2
Step-by-step explanation:
y=mx+b= 2
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Answer:
m = 2 and b = 9
Step-by-step explanation:
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Statement 1: If √12 - √8 = a, then √12 + √8 is equal to 4/a.
Statement 2: a + √b is called the rationalizing factor of c + √d if their product is 1.
• Statement 1 is true; Statement 2 is true; Statement 2 is the correct explanation of Statement 1.
• Statement 1 is true; Statement 2 is true; 2 is not the correct explanation of Statement 1.
• Statement 1 is true; Statement 2 is false.
• Statement 1 is false; Statement 2 is true.
It is an assertion-reasoning question. Please help me to solve this. Need step-by-step explanation as well. Thank you.
Answers
Answer:
Statement 1 is true; Statement 2 is false.
Step-by-step explanation:
Statement 1:
√12 - √8 = a
Let's use the given value of √12 + √8 ,that is, 4/ a.
If we multiply both the expressions such that their Left Hand Sides get multiplies together and Right Hand Sides together:
=> (√12- √8)(√12 + √8) = a × 4/a
On the LHS,
identity used:
(a-b)(a+b) = a²-b²
On the RHS:
a gets canceled due to its presence in both the numerator as well as the denominator.
=> 12 - 8 = 4
=> 4 = 4
That's it!
We got LHS = RHS, that approves the existence of the given statement.
___________________
Statement 2:
"a + √b is called the rationalizing factor of c + √d if their product is 1"
That's not entirely right!
The correct statement would be:
" a + √b is called the rationalizing factor of c + √d if their product is a rational number ."
Since, rationalizing has got nothing to do with 1, (1 is just another rational number), even if we get 2 by their multiplication, it will be called rationalizing as long as we're getting a rational number.
___________________
Answer:
Hence, I'd say:
Statement 1 is correct but Statement 2 isn't.
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Step-by-step explanation:
SInce the line crosses the y-axis at the point (0,4), and the line is positive since it is pointing upwards, and the slope of the line is 3 if you count up 3 over 1, the correct equation of the line is y=3x+4.
The pumpkin patch is open ever day. If it sell 2,750 pounds of pumpkins each day, about how many pounds does it sell in 7 days?
Answers
Answer:
19,250 I think.
Step-by-step explanation:
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[tex]8 = \dfrac{3+2x}{4+x}\\\\\implies 8(4+x) = \dfrac{3+2x}{4+x} \cdot (4+x)\\\\\implies 8\cdot (4+x) = 3+2x\\\\\text{Hence the answer is A.}[/tex]
Answer:
A
Step-by-step explanation:
8=3+2x/4+x
8/1= 3+2x/4+x then crisscross both sides without multiplying
8×(4+x)=3+2x
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Answers
Answer:
8/5
Step-by-step explanation:
You can rewrite the equation to 2/5 * 12/3
Which is equal to 2/5*4
So 2 times 4 is 8
So the answer is 8/5
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Ok done. Thank to me:>
Type: five-tenths=
Pls answer correctly fact practice math .
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Answer: 5-tenths= 5/10
Step-by-step explanation:
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First rearrange
5x-8y=-29
5x+29=8y
5/8x+29/8=y
Then sub in your x values
Step-by-step explanation:
5x-8y=-29
5(6)-8(5)
30-40
=-10
no
5(-9)-8(-2)
=-45+16
=-29
yes
5(-3)-8(1)
-15-8
=-23
no
5(0)-8(-4)
=0+32
=32
no
Write the equation of the line that passes through the point (4,5) and is perpendicular to the graph of y=2x-3
Answers
Hello there! :)
We are given that the line passes through the point (4,5) and that it's perpendicular to the line y=2x-3.
Perpendicular lines have slopes that are opposite reciprocals.
This means we take a number, make it negative, and flop it over:
2
-2
-1/2
So the slope of the line perpendicular to y=2x-3 is -1/2.
Now, we have the slope and a point that the line passes through, so we can write the equation in point-slope form, which looks like so:
y-y1=m(x-x1)
Where
y1 is the y-coordinate of the point
m is the slope
x1 is the x-coordinate of the point
Now, let's plug our values into the equation:
y-y1=m(x-x1)
y-5=-1/2(x-4)
y-5=-1/2x+2
y=-1/2x+2+5
y=-1/2x+7
Hence, that is the equation of the line.
Hope it helps.
~A lonely teen who helps others with a smile
-Grace :-)
Good luck.
what is the 60th term of the sequence 2, -3, -8, -13?
Answers
Answer:
-293
Step-by-step explanation:
The first term of the arithmetic sequence is a1 = 2. The common difference is d = -3-2 = -5. The general term is ...
an = a1 +d(n -1)
an = 2 -5(n -1)
The 60th term is ...
a60 = 2 -5(60 -1) = -293
Simply the Expression.
Answers
x
10
There’s something wrong with the question re check it