Question

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

I= -425x^2+45,500x-650,000.
According to this model, what is the maximum average annual income, in dollars, a lawyer can earn?

I got 54, is this correct?

Answer 1

differentiate and equate to zero

oh have you done any calculus?

Answer 2

I haven't done calculus. I'm in precalc right now but we're just learning about this stuff and it's really new to me s I'm just very confused.

Answer 3

ok this is a quadratic function whose graph is a parabola which will have a maximum value
and will be of the following form

Answer 4

oh - the draw function isnt working

it wil llook roughly like an upside down U

Answer 5

to find the maximum value you need to change it to the form

a(x + b) ^2 + c

Answer 6

i'm embarassed to say i've forgotten exactly how to do this
i can tell you though that the maximum value is 567,794 dollars at age 54