The function C (x) = 600x-0.3x^2 represents the total costs for a company to produce a product, where C is the total cost in dollars and x is the number of units sold. what number of units would produce a maximum cost?

C (x) = - 0.3x^2+600x

y=ax^2+bx+c

it shows a upside down parabola equation.

to find maximum value we need to find its vertex (h, k)

as this is a standard quadratic equation we need to see parabolis equation too

y=a (x-h) ^2+k

if u see this eq^n K would be the maximum value of Y if x=h.

where h, k are vertex of parabola.

h=-b/2a (derived standard formula)

C (x) = - 0.3x^2+600x

y=ax^2+bx+c

a = - 0.3 b=600

h=-600/-0.3

h = 2000

put h in place of x to get K

K = - 0.3 (2000) ^2+600 (2000)

K = - 1200000+1200000

K=0

u gets k=0

means C (x) = 0

600x = - 0.3x^2

600 = 0.3x

x=6000/3

x = 2000 units