The function C(x) = 600x – 0.3x2 represents 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?
What is the maximum cost?

Question

The function C(x) = 600x – 0.3x2 represents 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? 
What is the maximum cost?

Mercury · Answer

compare your function to the generic form ax^2 + bx + c to figure out your a, b, and c values

then x = -b/(2a) gives you the x-coordinate of your vertex (a.k.a the x-value that will maximize the cost function)

plugging in this x-value will give you the max cost

alternatively: if you know calculus, take the derivative, set it equal to 0 and solve for x. then repeat the step where you plug in x.