...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 ... tells you e = 150

f(60)=30 ... a(60^4) + b(60^3) + c(60^2) + d(60) + 150 = 30

df/dx (60) = 0 ... 4a(60^3) + 3b(60^2) + 2c(60) + d = 0

df/dx (180) = 0 ... same drill as above except w/ x = 180

df/dx (300) = 0 ... ditto w/ x = 300

solve for a, b, c, and d