Solving for multiple variables in a piecewise function

[heisenberg]

I need to solve for 11 variables in this piecewise function
............0.8x.................... if x<0
.............kx^3+Lx^2+mx+n, if 0<=x<=10
.....C(x)=ax^2+bx+c...........if 10<=x<=90
.............px^3+qx^2+rx+s...if 90<=x<=100
.............-1.6x+120............if x>=100

By finding both the first and second derivatives of each i am supposed to match up 11 equations, due to the fact there is 11 unknowns. It says the first and derivatives will give me 8 equations, and the following 3 will come from matching values of functions at 0,10,90. I literally have no idea what im doing but i need to solve for a,b,c,k,l,m,n,p,q,r, and s. Somebody please help me out?

 

[tkhunny]

Let's just work with the first two pieces.

............0.8x.................... if x<0
.............kx^3+Lx^2+mx+n, if 0<=x<=10

If we want it to be continuous at x = 0, we must have:

0.8x = kx^3+Lx^2+mx+n for x = 0, giving 0.8(0) = k(0)^3+L(0)^2+m(0)+n and 0 = n

If we want to match 1st derivatives at x = 0, we must have:

0.8 = 3kx^2+2Lx+m for x = 0, giving 0.8 = 3k(0)^2+2L(0)+m and 0.8 = m

If we want to match 2nd derivatives at x = 0, we must have:

0 = 6kx+2L for x = 0, giving 0 = 6k(0)+2L and 0 = L

There. We haven't even looked past x = 0 and we've already picked off three of the many mysterious numbers. See what you can do with x = 10.