1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
m_a_m_a [10]
3 years ago
12

Find a cubic function f(x) = ax3 + bx2 + cx + d that has a local maximum value of 3 at x = −3 and a local minimum value of 0 at

x = 1.
Mathematics
1 answer:
Amiraneli [1.4K]3 years ago
4 0

Answer:

The cubic function is f(x) = (27/32)·x  - 3/32·x³ - -9/32·x² - 9/32

Step-by-step explanation:

The given function is f(x) = a·x³ + b·x² + c·x + d

By differentiation, we have;

3·a·x² + 2·b·x + c = 0

3·a·(-3)² + 2·b·(-3) + c = 0

3·a·9 - 6·b + c = 0

27·a - 6·b + c = 0

3·a·(1)² + 2·b·(1) + c = 0

3·a + 2·b + c = 0

a·(-3)³ + b·(-3)² + c·(-3) + d = -3

-27·a + 9·b - 3·c + d = -3...(1)

a + b + c + d = 0...(2)

Subtracting equation (1) from equation (2) gives;

28·a - 8·b + 4·c = 3

Therefore, we have;

27·a - 6·b + c = 0

3·a + 2·b + c = 0

28·a - 8·b + 4·c = 0

Solving the system of equations using an Wolfram Alpha gives;

a = -3/32, b = -9/32, c = 27/32 from which we have;

a + b + c + d = 0 3 × (-3/32) + 2 × (-9/32) + (27/32) + d = 0

d = 0 - (0 3 × (-3/32) + 2 × (-9/32) + (27/32)) = -9/32

The cubic function is therefore f(x) = (-3/32)·x³ + (-9/32)·x² + (27/32)·x + (-9/32).

You might be interested in
What is the value of y?<br><br> Enter your answer in the box.
Dennis_Churaev [7]
You must know that the sum of interior angles is 180°. We also know that AC and BA are congruent which means angles B and C are also congruent. To find x we can assume 25=5x. Which makes x=5, and angle C=25°.

Then we can add all the angles to find y and A. 25+25+(3y+70)=180. Then solve for y and then solve for angle A.
5 0
3 years ago
Read 2 more answers
The store paid $2. 70 for a book and sold it for $6. 20. What is the profit as a percent?.
bogdanovich [222]

Answer:

profit = 129.63% (to the nearest hundredth) as a percent of the price the store paid for the book

Step-by-step explanation:

Use the percentage change formula:

percent change = [ (difference between the initial value and the final value) ÷ initial value] x 100

= [ (6.20 - 2.70) ÷ 2.70 ] x 100

= [ 3.5 ÷ 2.70 ] x 100

= 37/27  x 100

= 129.6296296...

= 129.63% (to the nearest hundredth)

5 0
2 years ago
How do you subtract nega
sergey [27]
Well think of it like this. lets say your teacher made you do this problem -48 - 10. I would just act like 48 is not an negative and add 10. After that I would put the negative back. So the answer would be -58. :P
3 0
3 years ago
Read 2 more answers
Find the total surface area of this triangular prism.
Irina18 [472]

Answer:

not sure but i think its 425 cm

Step-by-step explanation:

for the square i dont know

how its called in english the surface is 25×10= 250cm

and for the triangle its (25×14):2 = 175cm

so 175 + 250= 425cm

4 0
2 years ago
A painter starts with a blank 24-inch by 12-inch piece of rice paper. The painter wants to leave a uniform border x inches wide
ddd [48]

Answer:

a. A = x² - 36x + 288

b. If x = 2; A = 220 in²

Step-by-step explanation:

<h2>a.</h2>

In this scenario, 'x' represents the width of the border. A "uniform border" means that the border has the same width all around.

The area of the paper that can be painted does not include the border. Since the border is on the original rice paper (not added to it), you subtract 'x' from each side of the rice paper.

The area of a rectangle is A = lw (Area is length times width). <u>Each length and width is reduced by 'x'.</u>

If the original rice paper's area is: 24 X 12, then,

the Area that can be painted is:

A = (24 - x) (12 - x)

A polynomial in standard form means the most expanded version of an expression, ordering the terms (numbers) from greatest to least degree. (The degree of a term is the value of its exponent).

Expand the expression. Multiply the numbers from each bracket in the order FOIL (first, outside, inside last):

A = (24 - x) (12 - x)

= 288 - 24x - 12x + x²        Collect like terms (-24x - 12x = -36x)

= 288 - 36x + x²        Rearrange ordering greatest to least exponent value

= x² - 36x + 288        Standard form polynomial

<h2>b.</h2>

The width of the margin is the same thing as the width of the border. Since 'x' is the width of the border,

x = 2

Using either the expanded or factored equation for area of that can be painted, substitute 'x' for 2.

I will use the factored form.

A = (24 - x) (12 - x)        Substitute x for 2

= (24 - 2) (12 - 2)          Solve inside each bracket first by subtracting

= (22) (10)             Multiply

= 220                 Area that can be painted

Remember to include the units: 220 in²

Therefore if the margin is 2 inches wide, then the area that can be painted in 220 square inches.

5 0
3 years ago
Other questions:
  • The range of the function f(k) = k2 + 2k + 1 is {25, 64}. What is the function’s domain?
    15·2 answers
  • On a number​ line, A is at negative 7 and B is at 3. What is the coordinate of​ C, which is two fifths of the way from A to​ B?
    10·1 answer
  • What are the solutions to the equation 0=x^2+5x-6?
    8·1 answer
  • FAST PLEASE !!!!
    7·1 answer
  • Please help me with this math problem <br>Evaluate C/2 - 3 + 6/D when c=14 and d=3
    9·2 answers
  • What is the greatest number of bottles Corrine can put sand in?
    10·2 answers
  • Amy's car gets 32 miles per gallon. If her car's tank holds 15 gallons of gas, and she wants to keep a minimum of 1 gallon of ga
    6·1 answer
  • ANSWER ASAP PLZ!!!!<br><br><br> What type of roots would plants have in swampy, wetlands?
    11·2 answers
  • What's the conversion factor used to convert inches to yards?
    13·1 answer
  • The triangles are similar solve for x.
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!