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
Solve with completing the square method:<br>6x²-7x+2=0 and  ax²+bx+c=0
Norma-Jean [14]
6x ^2-7x+2=0\\ \\ a=6 , \ b = -7 , \ c=2 \\ \\\Delta = b^{2}-4ac = (-7)^{2}-4*6*2=49-48=1 \\ \\x_{1}=\frac{-b-\sqrt{\Delta }}{2a} =\frac{7-\sqrt{1}}{2*6}=\frac{7-1}{12} =\frac{6}{12}= \frac{1}{ 2}\\ \\x_{2}=\frac{-b+\sqrt{\Delta }}{2a} =\frac{7+\sqrt{1}}{2*6}=\frac{7+1}{12} =\frac{8}{12}= \frac{2}{ 3}


7 0
3 years ago
Please help!
Marat540 [252]

Answer:

y= 3(x+5)^2 -4

5 0
3 years ago
An angle that measures 89 degrees is called?
mafiozo [28]
An acute angle is any angle that is below 90 degrees, so 89 degrees is an ancute angle
5 0
3 years ago
What is the GCF of 48m5n and 81m2n2?
Lady bird [3.3K]
To find the GCF of the two terms, continuous division must be done.
What can be used to divide both terms such that there is not a remainder?
Start small, let's take 2. It could be a GCF.
Move up higher, say 3. Yes, it can be a GCF.
To see if there might be a greater common factor, divide the constants by 3.
48/3 = 16
81/3 = 27
Upon inspection and contemplation, there is no more common factor between 16 and 27. So, 3 is the GCF.

Moving on, when it comes to variables. The variable with the least exponents is easily the GCF. For the variable m, the GCF is m2 and for n, the GCF is n.

Combining the three, we have the overall GCF = 3m2n
7 0
3 years ago
Read 2 more answers
A ball is dropped from a height of 64 feet. Its height, in feet, can be modeled by the function h(t) = -167 + 64, where t is the
Oliga [24]

Answer:

Step-by-step explanation:

Known facts:

  • the ball dropped from a height of 64 feet
  • function h(t) = -16t^{2}  + 64

First question:

  • the ball hits the ground when h(t) = 0, thus we get the equation

                      -16t^{2} +64 = 0\\16t^{2} = 64\\t^{2} =4\\t = 2

     So the ball hits the ground in 2s

Second question

  • to find how long it takes the ball to fall 36 feet, we must set h(t) = 64 - 36 = 28

                      -16t^{2} +64 = 28\\16t^{2} = 36\\t = \frac{6}{4} =1.5s

      So the ball hits the ground in 1.5s

Hope that helps!

3 0
2 years ago
Other questions:
  • Timika wants to know the number of millimeters that are in 4.5 inches. What is the correct process for converting 4.5 inches to
    11·2 answers
  • Whart is 50x+56=<br><br><br><br> what is it!!
    8·2 answers
  • Brian and Mark are fishing. They both catch a fish. Brian's fish weighs 17
    14·2 answers
  • Elizabeth spent $77.69 at the school supply store. She then had $24.50
    15·1 answer
  • Write the equation of the line through the points (4,5) and (12,9)
    15·2 answers
  • Solve this 2 step equation <br> -2p + 12 &gt; 8
    10·2 answers
  • Given the equation 12x – 6y = –36, identify the slope and y-intercept.
    9·1 answer
  • HELP MEEEE I BEG U SO MUCH
    7·1 answer
  • What would be another way to write -8n-7
    7·1 answer
  • PLEASE HELP! ILL GIVE BRAINLIEST!I! I uploaded a picture below.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!