Question

The average annual income, I, in dollars, of a lawyer with an age of x years is modeled with the following function:

I=−425x^2+45500x−650000

According to this model, what is the maximum average annual income, in dollars, a lawyer can earn?

Round to the nearest whole dollar.

Answer 1

I = -425x^2 + 45500x - 650000
For I to be maximum, dI/dx = 0
dI/dx = -850x + 45500 = 0
x = 45500/850 = 53.53

Therefore, maximum I = -425(53.53)^2 + 45500(53.53) - 650000 = 567,794.11

Therefore, the maximum average annual income, in dollars, a lawyer can earn is $567,794