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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

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Anvisha [2.4K]

Answer:

6.7

Step-by-step explanation:

10% of 30000

10/100 x 30000

0.10 x 30000

=3000

In order to find how long you have to divide 20k with 3k

20000/3000 = 6.66666667

Round it up and you get 6.7

6 0
3 years ago
Consider the absolute value function f (x) = -|x + 2| - 2 . The vertex of the function is .
mezya [45]
The answer would be c
Hope this helps!
5 0
3 years ago
Find the difference. (7x-6 2/3) - (-3x + 4 3/4)
NikAS [45]

10x-61/12 is the difference of  (7x-6\frac{2}{3}) - (-3x + 4\frac{3}{4}).

<h3>What is Expression?</h3>

An expression is combination of variables, numbers and operators.

The given expression is (7x-6\frac{2}{3}) - (-3x + 4\frac{3}{4})

7x-6\frac{2}{3}+3x- 4\frac{3}{4}

7x-20/3+3x-19/4

Add the variable terms and constant terms.

10x-20/3-19/4

The LCM of 3 and 4 is 12/

10x-4-57/12

10x-61/12

Hence, 10x-61/12 is the difference of  (7x-6\frac{2}{3}) - (-3x + 4\frac{3}{4}).

To learn more on Expressions click:

brainly.com/question/14083225

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4 0
1 year ago
Write k divided by 11 is 7 in and equation
Ronch [10]

Answer:

k/11 = 7

Step-by-step explanation:

K is being divided by 11 and equals 7

5 0
3 years ago
Read 2 more answers
I need help with this​
Kruka [31]

Answer:

X=9/4

Step-by-step explanation:

-3x+10=5x-8

Subtract 10 from each sides

-3x=5x-18

Subtract 5x from both sides

-8x=-18

Divide both sides by -8

x=9/4

I hope this helped

3 0
2 years ago
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