Let f(x) = ax^4 + bx^3 + cx^2 + dx + e be the equation of the graph.

a,b,c,d and e are the unknowns.

Then 5 equations are:

f(0)=150

f(60)=30

df/dx (60) = 0

df/dx (180) = 0

df/dx (300) = 0

I'm not 100 percent sure on how to approach this. If anyone could give me a kick in the right direction it would be greatly appreciated.