In a certain company, the formula for maximizing profits is P = -25x^2 + 7500x,, where P is profit and x is the number of machines the company operates in its factory. What value for x will maximize P?
This one is from IntegratedLearning.
Here's what I did:
The OA states: To find a maximum or minimum value of an equation with an exponent in it, you take the derivative of the equation, set it to zero, and solve. I dont really get what that means. So whoever solves it, could you plz post explanation of what the above sentence mean as well? Choose one.
A) 10 B) 50 C) 150 D) 200 E) 300
Recognize that 25 is a factor of 7500. If we take this out, we have two parts to the equation:   -X^2300X   One part of the equation brings our value down, whereas the other part brings our value up. At this point, we can test the numbers in the answer choice. Notice that they are very straight forward to square, and multiplication by 300 is very easy.   A) 10 - 3000 - 100 = 2900   B) 50 - 15000 - 2500 = 12500   C) 150 - 45000 - 22500 = 22500   D) 200 - 60000 - 40000 = 20000   E) 300 - recognize that this is zero   Therefore, answer is 150.   Hope this helps those - like myself - who haven't thought about calculus for over half a decade.150
<result>C</result>
In a certain company, the formula for maximizing profits is P = -25x^2 + 7500x,, where P is profit and x is the number of machines the company operates in its factory. What value for x will maximize P?
This one is from IntegratedLearning.
Here's what I did:
The OA states: To find a maximum or minimum value of an equation with an exponent in it, you take the derivative of the equation, set it to zero, and solve. I dont really get what that means. So whoever solves it, could you plz post explanation of what the above sentence mean as well?