S.O.S. Mathematics CyberBoard

[pinkturtle]

I've been working on this recently but somehow i just couldn't understand the theory of it. could anyone please help with explanations ??

here's the questions.

Find the angle between the curves at their point of intersection:
a) to the right of the origin
b) to the left of the origin

1) y=4x² and y=(x-1)²

2) y=|x| and y=1/3(4-x)

millions thanks.

[Mona_]

I would assume that the question is asking about the angle between the TANGENTS to these curves at their point of intersection...

For the first pair; and

you first need to find the points of intersection, by solving their equations simultaneously.

You should get:





giving: or

Now the next step is to find the gradients at those points for each curve.
This is done by differentiation.

for the first graph:
and for the second:

At the first point where x=-1,
the gradients of the two graphs are: -8 and -4
To find the angle between them use the fact that the gradient of a line is the tangent of the angle it makes with the horizontal.

This means that gradient of each line

And so the angle between them is:

And you do the same for the second point of intersection.

As for the second set of equations it's easier, because they are already straight lines each with a known gradient (use two equations for , one is when x<0, and one is when x>0).

Can you continue from there???

[pinkturtle]

yes.
i finally got that.
=D

thanks alot !!