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yanalaym [24]
3 years ago
10

Find a cubic function f(x) = ax3 + bx2 + cx + d that has a local maximum value of 4 at x = −3 and a local minimum value of 0 at

x = 1.find a cubic function f(x) = ax3 + bx2 + cx + d that has a local maximum value of 4 at x = −3 and a local minimum value of 0 at x = 1.
Mathematics
1 answer:
Vinvika [58]3 years ago
8 0
The formula is f(x) = a x ^ 3 + b x ^ 2 + c x  + d 
f '(x) = 3ax^2 + 2bx + c. 
f(- 3) = 3 ==> - 27a + 9b - 3c + d = 3 
f '(- 3) = 0 (being a most extreme) ==> 27a - 6b + c = 0. 
f(1) = 0 ==> a + b + c + d = 0 
f '(1) = 0 (being a base) ==> 3a + 2b + c = 0. 
- 
Along these lines, we have the four conditions 
- 27a + 9b - 3c + d = 3 
a + b + c + d = 0 
27a - 6b + c = 0 
3a + 2b + c = 0 
Subtracting the last two conditions yields 24a - 8b = 0 ==> b = 3a. 
Along these lines, the last condition yields 3a + 6a + c = 0 ==> c = - 9a. 
Consequently, we have from the initial two conditions: 
- 27a + 9(3a) - 3(- 9a) + d = 3 ==> 27a + d = 3 
a + 3a - 9a + d = 0 ==> d = 5a. 
Along these lines, a = 3/32 and d = 15/32. 
==> b = 9/32 and c = - 27/32. 
That is, f(x) = (1/32)(3x^3 + 9x^2 - 27x + 15).
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I need some help on this math problem, thanks so much
bekas [8.4K]

Answer:

The answer is C.

Step-by-step explanation:

Hit 'em with the Law of Sines.

sin(A)/a = sin(B)/b.

Let's say x is equal to "A", thus 5 is "a".

sin(x)/5 = sin(B)/b.

We could go for the obvious choice for "B", which would be the 90 degrees shown. To solve for the hypotenuse which will be "b", let's use the Pythagorean Theorem:

a^2 + b^2 = c^2

5^2 + 20^2 = c^2

25 + 400 = 425

sqrt(425) = about 20.6, which we can now substitute "b" with.

sin(x)/5 = sin(90)/20.6

sin(x)/5 = 1/20.6

sin(x)/5 = 0.04854...

sin(x) = 0.2427...

You can plug in sin^-1(0.2427) into your calculator, and you should end up with something like 14.047... which equates to answer choice C.

6 0
3 years ago
...................
Zinaida [17]

Answer:

easey, sub them

(x,y)

see if true

(0,1), 2(0)+1>-4, 1>-4, true

(4,-12), 2(4)+-12>-4, 8-12>-4, -4>-4, false

(5,-12), 2(5)+-12>-4, 10-12<-4, -2>-4, true

(-1,-1), 2(-1)+-1>-4, -2-1>-4, -3>-4, true

(-3,0), 2(-3)+0>-4, -6>-4, false

answers are

(0,1)

(5,-12)

(-1,-1)

Hopefully that helped you a little bit :)

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Answer:

1-k^2

Step-by-step explanation:

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(sin A)(cos A)(sin A/cos A)=(sin A)^2

(sin A) ^2 + (cos A) ^2= 1

(sin A) ^2=1-(cos A) ^2

(sin A)^2= 1 - k^2

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