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.
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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).
Answer:
x=3; y=3
Step-by-step explanation:
y = -1/2 x + 9/2
so if we multiply by 2 on both sides
2y = -x + 9
and we know that y = 3x-6
so we get
2(3x-6)=-x+9
6x-12 = - x + 9
7x = 21
x = 3
y = 3 * 3 - 6
y=3
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x=3, y=3
You put them in the equation and they should work.
=D
Explanation:
To write an equation from logarithmic form to exponential form, we will use the following
Then, the given equation can be written as
Answer:
Therefore, the answer is
Answer:2,7,12,19
Step-by-step explanation:
a2=a2-1+5=-3+5=2
a3=a3-1+5=a2+5=2+5=7
a4=a3+5=12 and continue so on
