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
8090 [49]
2 years ago
10

Find a cubic function f(x) = ax^3 + bx^2 + cx + d that has a local maximum value of 3 at x = −3 and a local minimum value of 0 a

t x = 1.
Mathematics
1 answer:
Ahat [919]2 years ago
3 0

Answer:

f(x) = (3x³ + 9x² - 27x + 15)/32

Step-by-step explanation:

f'(x) = 3ax² + 2bx + c

Maximum or minimum: f'(x) = 0

Maximum: f'(-3) = 0 and f(-3) = 3

Minimum: f'(1) = 0 and f(1) = 0

f'(-3) = 0 leads 27a - 6b + c = 0       (1)

f'(1) = 0 leads 3a + 2b + c = 0           (2)

f(-3) = 3 leads -27a + 9b -3c + d = 3    (3)

f(1) = 0 leads a + b + c + d = 0        (4)

(1) - (2):   24a - 8b = 0, or 3a - b = 0, b = 3a

(3) - (4)   -28a + 8b - 4c = 3    (5)

(1) * 4 + (5):  80a - 16b = 3,

use b = 3a, get 80a - 16*3a = 3, 32a = 3, a = 3/32, b = 3a = 9/32

From (2): c = -3a - 2b = -9/32 - 18/32 = -27/32

From (4): d = -a - b - c = -3/32 - 9/32 + 27/32 = 15/32

So

f(x) = (3x³ + 9x² - 27x + 15)/32

You might be interested in
How do you solve this problem.
Nat2105 [25]

Answer:

8 were yoused  because 8 times 3 =24 so if you subtract you get 8

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
About how many cells are in the human body?
Mrrafil [7]

I think its 30 trillion cells

hope it helps

5 0
2 years ago
Answer i will mark as brilliant <br><br><br> plssssss answerrrr<br> plsssss<br> plssss<br> answer
Free_Kalibri [48]

Answer: Option 2.

Step-by-step explanation:

a fraction is a way of showing division. b divided by 8 can also be shown as

b

_

8

6 0
3 years ago
Read 2 more answers
Volume &amp; surface! May I please have help
Ludmilka [50]

Answer:

D

Step-by-step explanation:

surface area of cylinder

=(area of base)×2 + (area of curved surface)

=(\frac{20}{2} )^{2} \pi× 2 + 20\pi × 25

=2 × \pi × 10^{2} + 2 × \pi × 10 × 25

3 0
2 years ago
the cost of a ticket t to a concert with a 3% sales tax can be represented by the expression t+0.03t. simplify the expression. t
Leokris [45]
.03 time 72 then add 72 or just do 1.03 time 72
4 0
3 years ago
Other questions:
  • Write an equivalent expression to 9y -1/2(4y+20)
    11·2 answers
  • Terrance Jacobs is looking for a larger home. Jacobs offers $205,000 for a fourbedroom house and the seller accepts. Jacobs wish
    6·1 answer
  • PLEASE HELP ME W/ MATH ASAP!!
    8·2 answers
  • Suppose you have a drawer full of white, black, and yellow pairs of socks. If the probability of picking a white pair of socks i
    6·1 answer
  • Find the work done by the force f(x)=3x+7 in moving a particle from x=1 to x=3
    9·1 answer
  • On August 1, 2021, a company accepts an $8,000, 9-month note receivable. For 2021, the company reports interest revenue of $200.
    15·1 answer
  • Which property is best used prove a quadrilateral is a rectangle?
    13·1 answer
  • Which equation is equivalent to y−3=4(x−5)?
    7·2 answers
  • The sale price of a new refrigerator is $705 and sales tax is figured at 0.05 times the price. What is the total amount paid for
    10·1 answer
  • Brendan created a connect-the-dots puzzle in the shape of a square for his little brother. He plotted dotson a coordinate plane
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!