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
