Lagrange Multipliers

[Guest]

Hi everyone
I was just wondering if there was a trick to knowing how many points that you are going to come out with? I remember something from precal with quadratic equations...like if there is x^4... then there are 3 real roots with n-1..something like that. I don't even know if I'm saying that right.

So basically I'm looking for a short cut on how to figure out how many critical points I'm going to find.

Thanks
Take care,
Beckie

 

[sco11]

Right, if it's like x^4...... then there will be three curves in the graph. Of course x^4 alone is not a very good example, but as you said it has to be a quadratic. By 3 curves i mean 2 maximums and one minimum, or 1 minimum or 2 maximums, whatever.

 

[stapel]

if it's like x^4...... then there will be three curves in the graph.

Maybe. There won't be more than three curves, but there might be only one, such as is the case for f(x) = x⁴ or g(x) = (x + 2)⁴.

In general, one takes the degree "n" of the polynomial and concludes that there will be no more than n zeroes (crossings of the x-axis) and there will be n - 1, n - 3, ... "turnings" of the graph. (If n is odd, there may be no places where the graph turns back on itself; if n is even, there will be at least one, but perhaps no more.)

Eliz.

 

[Guest]

Thank you!