Question

the function f(x)=6x^2-180x=1000 represents the profit f(x) in thousands of dollars of selling x items. what is the meaning of the extreme value

Answer 1

To find the extreme value of the function f(x) = 6x^2 - 180x + 1000, we can first take the derivative of the function and set it equal to zero:

f'(x) = 12x - 180 = 0

Solving for x, we get x = 15. Substituting this value back into the original function, we get:

f(15) = 6(15)^2 - 180(15) + 1000 = 1250

So the extreme value of the function is 1250, which represents the maximum profit in thousands of dollars that can be earned by selling a certain number of items.

More specifically, the value x = 15 is the value of x that maximizes the profit, and the maximum profit is $1,250,000. This means that if the company sells 15 items, they will make the most profit possible.

Explanation: