Finding Intersections: Solving 4x-x^2=3

[jmanna98]

Can someone please help me with some algebra. I need to find the intersections of 2 functions so that I can find the volume using cylindrical shells and I have become pretty rusty when graphing the functions. When setting the functions equal to each other I get:

4x-x^2=3

Now I forget, do I just try solving for x (which I can't figure out how to do) or can I bring everything over to one side and set it equal to zero ...(or is that just going to find the roots?)

How should I do this?

 

[chiro]

Hey jmanna98 and welcome to the forums.

To find the intersection of two functions you just equate them together. Doing this depends on the representation of the function.

For example if you have two functions that are represented as y = bla1 and y = bla2 then basically you just use the fact that bla1 = blah2 and then solve for x. If x is a complicated expression then you will need to use a computer to get an approximate answer.

If however it is implicit (like say x^2y + x^5 x SQRT(y) = 3), then you have to do a bit more work, but the idea is the same: get one equation in terms of the other, rearrange and then solve for one variable which might mean using a root-finding algorithm).

 

[jmanna98]

Thanks for that. Much appreciated.