The function f(x) = A * x ² + Bx + C has a local minimum at 0, and its graph contains the points (0,2)and (1,8). Find A, B, and C. 6. For the function f(x) = a * x ³+ b * x ² , find a and b so that the point (1,6) is an inflection point of f.

Answers

Answer 1

Answer:

Final answer:

The values A, B, and C for the first function are 6, 0, and 2 respectively. For the second function, a = 6, b = 0.

Explanation:

Since the function f(x) = Ax² + Bx + C has a local minimum at 0, then B = 0, because the derivative of a quadratic is 2Ax + B, and this must equal 0 if there's a local minimum. The function contains the point (0,2), giving us C=2. It also goes through (1,8), which gives us the equation A + 2 = 8, or A=6.

For f(x) = ax³ + bx², the inflection point formula gives 2b = 0, meaning b=0. Since the point (1,6) is on the graph, we can substitute into the equation to find a = 6.

Learn more about Quadratic and Cubic Functions here:

brainly.com/question/32582937

#SPJ11

Related Questions

Entre os alunos que frequentam o Ensino Profissional na escola do Carlos foi recolhida umaamostra de 50 aos quais se colocou a questão:«Qual das seguintes frases exprime melhor o teu gosto pelo estudo da Matemática?Gosto muito.Gosto de certos conteúdos.Gosto pouco.Não gosto nada.»O seguinte gráfico traduz as respostas obtidas à questão anterior.1.1. Indique a variável em estudo e a sua natureza.1.2. Calcule a percentagem de alunos que responderam «Gosto muito».1.3. Observe a seguinte tabela ainda referente à mesma questão.RapazesRaparigasGosto muito126Gosto de certos conteúdos87Gosto pouco66Não gosto nada23Escreva um pequeno texto no qual justifique que, neste estudo, os rapazes mostraram ter um maior gosto pelo estudo da Matemática
Is 0.02 irrational or rational
if the perimeter of a circular sector is fixed at 100 ft, what values of r and s give the sector the greatest area? ...?
Which of the following represents the graph of f(x) = 4x − 2? graph of exponential rising up to the right, through the point 0, negative 3 graph of exponential rising up to the right, through the point 0, 1 graph of exponential rising up to the right, through the point 0, 3 graph of exponential rising up to the right, through the point 0, negative 1
I'd seriously appreciate it if anyone could help ASAP! I'm giving Brainliest!The point (-6, y) lies on the graph of the equation: 5y=2x−4.What is the value of y?--I believe it is but I'm not sure.

Round 8,031,426,100. Write the result as the product of a single digit and a power of 10.

Answers

Answer:

Step-by-step explanation:

8,031,426,100

=8,000,000,000

=8×(10)^9

Which of the following equations is an equation formed when completing the square on y 2 - 12y = -27?(y - 6) 2 = -27
(y - 6) 2 = 9
(y + 6) 2 = 9

Answers

Answer: The correct option is

(B) $(y-6)^2=9.$

Step-by-step explanation: We are given to select the equation that is formed when completing the square on the following equation :

$y^2-12y=-27~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We will be using the following formula :

$a^2-2ab+b^2=(a-b)^2.$

From equation (i), we have

$y^2-12y=-27\n\n\Rightarrow y^2-2* x*6=-27\n\n\Rightarrow y^2-2* x* 6+6^2=-27+6^2\n\n\Rightarrow (y-6)^2=-27+36\n\n\Rightarrow (y-6)^2=9.$

Thus, the required equation that is formed is $(y-6)^2=9.$

Option (B) is CORRECT.

Hello,

You should write y²-12y=-27 or y^2-12y=-27

y²-12y=-27
==>y²-2*6y+6²=-27+36
==>(y-6)²=9
(second answer)

Jerry ate 1,070 calories total at breakfast. He ate a cup of yogurt that had 150 calories in it and some granola. Each cup of granola has 230 calories. how many cups

Answers

Answer:

4 cups that's how many cups Jerry ate

Megan borrowed $50,000 at 5% simple interest for 6 years. joseph borrowed $60,000 at 4% simple interest for 8 years. using the formula who will have a greater monthly payment, m, and by how much?

Answers

Answer:

Megan will pay $78 more than Joseph.

Step-by-step explanation:

Formula: Simple Interest = P x R x T

Megan Info

Borrowed Money (P)=$50,000
Rate of interest (r)=0.05
Time (t) = 6 years

Simple interest paid by Megan = 50,000 x 0.05 x 6 = 15000

Total amount paid in 6 years = 50000 + 15000 = $65,000

Monthly payment by Megan (m) = 65000÷72 = $903

Joseph Info

Borrowed Money (P)=$60,000
Rate of interest (r)=0.04
Time (t) = 8 years

Simple interest paid by Magan = 60,000 x 0.04 x 8 = 19200

Total amount paid in 8 years = 60000 + 19200 = $79,200

Monthly payment by Joseph (m) = 79200÷96 = $825

Now we find Difference of monthly payment

⇒Megan - Joseph

⇒ 903-825

⇒ $78

Thus, Megan will pay $78 more than Joseph.

Answer:

Megan will pay approximately $78 more per month.

Step-by-step explanation:

32 ft/sec to meters/min

Answers

Its 585.216 meters/min

A circle has a circumference of 196π
What is the radius of the circle?

Answers

Circumference=2πr
196π=2πr. Divide both sides by 2π so the answer is 98

Other Questions

The formula below gives D, the demand for concert tickets when the price of each ticket is P dollars. D(p)=2000-4p-p^2What's the value if D(15)

Find the 95% confidence interval for a sample of size 358 with 13% successes. A) (0.0973, 0.1627) B) (0.1156, 0.1444) C) (0.1257, 0.1343) D) (0.1378, 0.1222)

2(4 + 2x) ≥ 5x + 5? please help

If X=3, What is the area of a triangle with sides, 6x ,7x, and 21x? A.117 in² B.378 in² C.189 in² D. 58.5 in²