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An alternative method of getting an approximate root of your cubic is to note that, from the graph it is clear that the solution lies between -2 and -2.5. Keep guessing values in between and try them in the cubic to see how close to zero you can get. The human brain is good at this sort of guesswork, and it probably won't take many guesses to get several decimal places of accuracy!

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The Newton Raphson formula is an iterative one. You plug your initial guess x₀ into the right hand side to get a better estimate x₁.  You then plug x₁ into the right hand side to get an even better estimate x₂.  You repeat this process a few times until two successive estimates are the same to within the accuracy you are working to.

To get the turning points use the quadratic equation to get the roots:

x_min = (-6 - sqrt(6^2 - 4*3*2))/(2*3)

x_max = (-6 + sqrt(6^2 - 4*3*2))/(2*3)

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I'm sorry I don't understand the formula you're using there.

The exact task is to approximate the local max and local min (I didn't mean the - or + infinite parts) and to approximate the coords of intersection points.

Like at this point in time I'm not "supposed" to know how to find the exact coords, as it's part a math class. 

Only tools I have is finding roots the basic way if a>1 or Gauss (wich doesn't work because the constant here is 1).

So as of now I have this:

(0,1)

approx: (-2.25,0)

Local (or relative) minimum: approx (0.4, 0.55)

Local (or relative) maximum: approx (-1.5 , 1.375)

4.   f(x) = 5x+ 3.  g(x) = (2x- 1)/3

f(g(x)) = 5*(2x- 1)/3 + 3 → 10x/3 + 4/3

5. Yes

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Subtract 69.093 from both sides

4.9303ln(x) = (94.59-69.093)

Divide both sides by 4.9303

ln(x) = (94.59-69.093)/4.9303 ≈ 5.17149

Exponentiate both sides

x  = e^5.17149 ≈ 176.2

Solve for x:
94.59 = 69.093+4.9303 log(x)

94.59 = 9459/100 and 69.093+4.9303 log(x) = 69093/1000+(49303 log(x))/10000:
9459/100 = 69093/1000+(49303 log(x))/10000

9459/100 = 69093/1000+(49303 log(x))/10000 is equivalent to 69093/1000+(49303 log(x))/10000 = 9459/100:
69093/1000+(49303 log(x))/10000 = 9459/100

Subtract 69093/1000 from both sides:
(49303 log(x))/10000 = 25497/1000

Multiply both sides by 10000/49303:
log(x) = 254970/49303

Cancel logarithms by taking exp of both sides:
Answer: |x = e^(254970/49303)

1,482 =1482 = 2 * 3 * 13 * 19 These are PRIME factors of 1,482. Multiples of 1,482??. Just multiply it by any number that you want.

Diagonal = sqrt( (15-3)^2 + (14-5)^2 ) → 15.36 inches

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Are you thinking of "Linear Equation"?

So you can learn the "general concept" of indices or exponents.

It looks like "C"

To find the turning points (not the maximum, that's clearly infinity, nor the minimum, that's clearly -infinity) set dy/dx equal to zero and find its roots:

3x^2 + 6x + 2 = 0

This will give you the values of x where the turning points occur.

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Just divide: 140 /2 =70 km/ph

Interest = Principal x Interest rate(as a decimal).

But, it can get more complicated than that depending whether you are calculating "simple interest" or " compound interest".

You will need a numerical method to find the root. One possibility is the Newton-Raphson method:

y(x) = x^3 + 3x^2 + 2x + 1

dy/dx(x) = 3x^2 + 6x + 2

Start with an initial guess of x₀ (say, -2.5)

Then use the following iterative process:  x_n+1 = x_n - y(x_n)/dy/dx(x_n) repeatedly until you get a sufficiently accurate result.

Thanks a lot!

Although, I have the find some exact coords:

I found x=0 which is (0,1)

But I have to find y=0

That is why I'm trying to find it's root.

I also have to find the minima and maxima.

The polynomial  x^3 + 3x^2 + 2x + 1 has just one real root, and doesn't factorise nicely - see the graph below:

Are you looking for percentage?

I am so sorry.

I just noticed I forgot a "+1" at the end of the polynomial.

That would be :

x^3 + 3x^2 + 2x + 1

Honestly I didn't fully get what you meant there. But my question is this:

If you say x=0 as in "x" is a potential rationnal root of the polynomial, wouldn't it mean that you have divided said polynomial by 0 in the first place?

But obviously we can't divide by 0...

So yah, the x=0, I just don't get it.

You dreamt of this one in your own head!. There is NO SOLUTION for it.