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Re: Math Homework

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GeoVolcano is not online. GeoVolcano
Joined: 05 Jul 2012
Total Posts: 1433
11 May 2015 06:38 PM
Is there a tangent line for:

f(x) = x^3 + 6x^2 + 21x + 26?

When I did it, I got 3x^2 + 12x + 21 which has imaginary roots.

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Sandykinz is not online. Sandykinz
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11 May 2015 06:41 PM
use wolframalpha
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FleskhjertaOwns is not online. FleskhjertaOwns
Joined: 15 Sep 2008
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11 May 2015 06:41 PM
SANDTROOPER PLEASE LOL
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ilezybet is not online. ilezybet
Joined: 02 Jan 2014
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11 May 2015 06:42 PM
use wolframalpha [2]
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renamed2163391 is not online. renamed2163391
Joined: 26 Oct 2014
Total Posts: 2403
11 May 2015 06:43 PM
8 x 3 = 24 + 1 =25 + 3 + 2= 30

Renamed2163391 - Acclaimed RTer
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GeoVolcano is not online. GeoVolcano
Joined: 05 Jul 2012
Total Posts: 1433
11 May 2015 06:43 PM
Well apparently I was correct for the derivative. That was an easy problem.
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LegoADS is not online. LegoADS
Joined: 03 May 2011
Total Posts: 25703
11 May 2015 06:43 PM
f(x) = x^3 + 6x^2 + 21x + 26?


is this an equation of a circle? or this is just a tangent with the radius of a circle??

a^2+b^2=c^2

so

7^2+21^2=26^2 i believe
so if these are equal then it is a tangent


441 = 7^2+21^2
26^2 = 676


so i think the answer is no...

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LegoADS is not online. LegoADS
Joined: 03 May 2011
Total Posts: 25703
11 May 2015 06:45 PM
ok i have no idea what ive done i will have to look into this more
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GeoVolcano is not online. GeoVolcano
Joined: 05 Jul 2012
Total Posts: 1433
11 May 2015 06:46 PM
Yeah I plugged the equation into the quadratic formula and it had imaginary roots.
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GeoVolcano is not online. GeoVolcano
Joined: 05 Jul 2012
Total Posts: 1433
11 May 2015 06:46 PM
Also yeah you don't know what you are talking about lol.
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LegoADS is not online. LegoADS
Joined: 03 May 2011
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11 May 2015 06:49 PM
ok so

'Both the graph of y = f(x) and the tangent line pass through the point, and the tangent line has the same gradient, 'm', as the function at that point.'

f(x) = x^3 + 6x^2 + 21x + 26

ok so y = m(x-x1)+y1

ok this is confusing so

y =

so basically you would have to work out the gradient and probably do a table of results for each x and y value and put that in the equation to find the point of the tangent
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Mathfreak231 is not online. Mathfreak231
Joined: 21 Jun 2010
Total Posts: 5311
11 May 2015 06:54 PM
yes it has "a tangent line"
in fact it has infinite tangent lines, one at each value of x
fail

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GeoVolcano is not online. GeoVolcano
Joined: 05 Jul 2012
Total Posts: 1433
11 May 2015 06:56 PM
@MathFreak, would it be:

x = +- i

y = +-21i +-i + 26 +-6

and therefore have (-infinity, +-i), (=-i, infinity) for the areas of increase and decrease of the equation?
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LegoADS is not online. LegoADS
Joined: 03 May 2011
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11 May 2015 06:57 PM
so you pretty much have to work out the point the tangent meets the curve and then find the normal which is the perpendicular line to the tangent

like math said there should in theory be an infinite number of tangents that can meet the curve??? is there any extra info
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LegoADS is not online. LegoADS
Joined: 03 May 2011
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11 May 2015 06:59 PM
o im 15 so ive covered like none of that

that looks beyond or roughly A-level standard
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Sandykinz is not online. Sandykinz
Joined: 14 Aug 2008
Total Posts: 81620
11 May 2015 06:59 PM
what is all this fuss about
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GeoVolcano is not online. GeoVolcano
Joined: 05 Jul 2012
Total Posts: 1433
11 May 2015 07:00 PM
Oh wait, isn't the slope for the max and min of the graph 0?
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Mathfreak231 is not online. Mathfreak231
Joined: 21 Jun 2010
Total Posts: 5311
11 May 2015 07:13 PM
if your derivative has all imaginary roots that simply means that the slope of the polynomial is never zero

but it still has a derivative

i'm not huge on calc yet but that's what i'm going for

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GeoVolcano is not online. GeoVolcano
Joined: 05 Jul 2012
Total Posts: 1433
11 May 2015 07:26 PM
Yeah I got the derivative, but I have to find the max and min by using it. As well as the value and location. So all of my answers look completely weird.
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Mathfreak231 is not online. Mathfreak231
Joined: 21 Jun 2010
Total Posts: 5311
11 May 2015 07:27 PM
well like i said the derivative is never 0 so there are no mins/maxs

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