How to get the largest positive root of a polynomial

Hi,

If I have found the roots of a polynomial using allroots() are the roots 
given in any particular order?

If not how can I sort the list to get the largest positive root?

Here's what I want to do:

I have a cubic which has been fitted to some experimental material test 
data, but the fit is poor at low values of x so I'm trying to define a 
piecewise function which is linear for low values and cubic otherwise. 
I've chosen to make the linear part tangent to the cubic.

The fitted cubic is:

(%i1) f(x):=4970*x^3 + 6320*x^2 - 425*x + 26;
                                 3         2
(%o1)             f(x) := 4970 x  + 6320 x  + (- 425) x + 26

I can find the tangent of a line through 0,0 andthe cubic:

(%i2) a:allroots(f(x)-diff(f(x),x)*x);

(%o2) [x = .06125686127110409, x = - .06786377328650396,
                                                        x = - 
.6292079773206162]

Now I can define the piecewise function, but this assumes that the roots 
list is sorted in descending order.

(%i3) g(x):=block(u:rhs(a[1]), if(x 07 8627077
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