Maths ! help !

[Anjali]

And for ques 1 , have you just substituted y=mx+c in the hyperbola equation ? Actually Iam trying that ways but it has become very complicated.

[Granpa Simpson]

Thanx Anjali..!!!
Upwards concave means the slope term goes on increasing which implies f''(x)is >=0, so you just differentiate the twice and set f''(x)>=0, you will get the answer.
For that Euler theorem part you take the general form of Euler's theorem, because if you prove that for a single functional form then you wont be able to generalize the result, so its better that you start with the general form...

[Anjali]

But for concave , don't we take 2nd derivative as less than 0 ?
And for concave downwards , 2nd derivative less than 0 ?
What about convex then ? It's so confusing !

[The Villain]

For quest 4 a simple trick is
Find double derivative and eqaute to zero...draw the sign scheme...if negative to postive then it is convex and if the sign changes fr postive to negative then it is concave

[Granpa Simpson]

Concave upwards and convex functions are the same...in concave upward function the slope goes on increasing..so the second derivative is set at greater than or equal to zero...and for concave down it is the opposite..:)

[Anjali]

Thanks for that Euler theorem question - done !

[Anjali]

Ron please exemplify your statement ! Iam confused !
Take this equation
Y=2-x^2
Now 2nd derivative is -2 , so it's concave - but what's all this downward and upward ???
And please try question 1 - that hyperbola one !

[Granpa Simpson]

In that question you will just have to find the domain of x for which the function is convex...just find out that and you will get the answer..this is because concave upward implies convexity..!!!

[The Villain]

Concave upward/convex downward means convex
concave downward/convex upward means concave
Given ur ques 2x - 6 x^2

f " is 2-12 x
put it 0
x is 1/6
make sign diagram..way curve and check for sign scheme
for x<1/6 it is +ve
and vice versa
so sign changes fr positive to negative so fn is concave.

[Granpa Simpson]

The hyperbola one is a theorem, just remember the conditions for a line to cut a hyperabola once, twice and at no point..the proof is quite tedious..ul have to proceed by considering the eccentricity of an ellipse and then changing it for a hyperbola case..its a bit complicated..better to remember the condition..!!!

[Homer Simpson]

check this out :)

[Deepak_Ka]

Came across this ques in IGIDR sample paper:

x=sin(2pie/7)+sin(4pie/7)+sin(8pie/7)
y=cos(2pie/7)+cos(4pie/7)+cos(8pie/7)

The value of x^2+y^2 is :
a.2
b.3
c.4
d.1
e.NOTA

Answer is : a.)2

How do I go about exactly so that in x^2+y^2 I have no term involving the angle is sin or cos in form of pie/7??

[Ashima]

This must be in the advanced maths section? Isn't it?

[Shefali]

yup,it is advanced maths section .

[Ashima]

Thank god! Trigno wasnt there is the mathematical part for eco students! Right?

[Shefali]

Ya right ashima..