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2 unit maths revision (1 Viewer)

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my school is behind in this topic, so im trying to accelerate. that's why i asked this question, cause im not completely sure how to do it with confidence
 

SpiralFlex

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my school is behind in this topic, so im trying to accelerate. that's why i asked this question, cause im not completely sure how to do it with confidence
Curve is increasing. (Curve going down at a particular range)
Curve is decreasing. (Curve going up at a particular range)
Curve stationary. (Curve not moving at all at particular points)

Step 1: Differentiate.

Step 2: For stationary points make

Step 3: Solve.

Step 4: Substitute back into ORIGINAL equation.

Step 5: You have your stationary points. :)
 
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SpiralFlex

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No worries, I have nothing better to do on a Saturday night anyway.
 

hscishard

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P(x)=ax^3+bx^2+cx+d P(0) = 5 = d
P'(x)=3ax^2+2bx+c
0 = 3ax^2 + 2bx + c for stat points.
0 = 3a + 2b + c 0 = 12a - 4b + c
12a - 3a - 4b -2 b + c - c = 0
9a - 6b = 0
3a - 2b = 0
P(1) = 12 P(-2) = 15
Hence, a + b + c + d = 12 -8a + 4b - 2c + d = 15
a + 8a + b - 4b + c + 2c + d - d = 12 - 15
9a - 3b + 3c = -3
3a - b + c = -1
3a - 3a + b + 2b + c - c = 0 + 1
3b = 1
b = 1/3
9a - 5(1/3) = 0
9a = 2.5
a = 5/27
3(5/27) - 1/3 + c = -1
c = -1 - 15/27 + 1/3
c = -11/9
a + b + c + d = 12
5/27 + 1/3 - 11/9 + d = 12
d = 12 - 5/27 -1/3 + 11/9
This is wrong... lol
lol: know yu cant said 2, unit mths is piss esy

Lmao
 

HSCAREA

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(x+2)^2 = 4x-x^2
Then solve
x^2 +4x + 4 = 4x - x^2

4x = 4x - 4

x = x - 1 the fuck?


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(x+2)(x+2) = x^2 + 4x + 4

therefore x^2 + 4x + 4 = 4x - x^2
2x^2 + 4 = 0

therefore 2x^2 = -4

x^2 = -2

x = sqroot -2

= no real roots the fuck?
 
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(x+2)(x+2) = x^2 + 4x + 4

therefore x = 4x - x^2 - 2
lol thats the worst display of algebra I have ever seen

ab=0

means a=0 or b=0

that only works when a product equals zero!! : (

EDIT: but even if you were trying x+2 = x^2 + 4x+4 that would give x= x^2 +4x + 2

lolz so many mistakes
 

benji_10

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The solution is in the complex field, which is 4U. I thought this was 2U revision?
 

hscishard

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Sorry, I didn't see the function correctly.
(x+2)^2 = 4-x^2
Since I've caused you some confusion, i'll post the solution

x^2 + 4x +4 = 4-x^2
2x^2 +4x = 0
x=0 and -2. Check by subbing it back into each function to make sure they yield the same value. In this case they do.

Now it's
You can calculate the first one quite easily. It's just 1/4 of the area of a circle. The radius is 2, so pi(2)^2 / 4 = pi
Now it's

The integral isn't hard to find, i'll assume you know how to do it.
The answer should be pi-2
 
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lalala369

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differentiate <a href="http://www.codecogs.com/eqnedit.php?latex=\displaystyle x\sqrt{x@plus;1}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\displaystyle x\sqrt{x+1}" title="\displaystyle x\sqrt{x+1}" /></a>
 
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differentiate <a href="http://www.codecogs.com/eqnedit.php?latex=\displaystyle x\sqrt{x@plus;1}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\displaystyle x\sqrt{x+1}" title="\displaystyle x\sqrt{x+1}" /></a>
 

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