Solving the result of a derivative: cost=0.04q^3-0.9q^2+10q+5

Amber12

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I am taking an econometric class and some things are a little bit over my head. I'm studying about maximizing net benefits and the original information is that cost=0.04q^3-0.9q^2+10q+5. Is asking to find the value of q that optimizes this function. So I assume I should calculate the first derivative and consider that it equals zero ???... well if I do that I get 0.12q^2-1.8q+10=0
Well I don't know how to find the values of q :(
Can somebody please explain how to solve this?
Thank you
 
0.12q^2 - 1.8q + 10=0
Well I don't know how to find the values of q :(
Can somebody please explain how to solve this?
Are you familiar with the Quadratic Formula?

This equation is second-degree polynomial (aka: quadratic polynomial) equation. The Quadratic Formula is one way, and it's guaranteed to find the solutions.

Some students would first multiply each side of the equation by 100, to convert the decimal numbers into Integers, but it's not necessary.

If you need to, google keywords introduction to quadratic formula, to view lessons, examples, and video lectures. :cool:
 
Are you familiar with the Quadratic Formula?

This equation is second-degree polynomial (aka: quadratic polynomial) equation. The Quadratic Formula is one way, and it's guaranteed to find the solutions.

Some students would first multiply each side of the equation by 100, to convert the decimal numbers into Integers, but it's not necessary.

If you need to, google keywords introduction to quadratic formula, to view lessons, examples, and video lectures. :cool:


I am somewhat familiar and I did google and looked into quadratic formula. However, since I can't break the equation really easy in two factors and find out the values of q...i don't know how is the best way to do it.
 
I am somewhat familiar and I did google and looked into quadratic formula. However, since I can't break the equation really easy in two factors and find out the values of q...i don't know how is the best way to do it.
Then try using the Quadratic Formula! (here) ;)
 
Yes. I did. Thank you for the help.
I found no solution for the equation since b^2-4ac<0.
Good for you!

That equation actually has two solutions, but they are Complex numbers, instead of Real numbers. So it's more accurate to say, "I found no Real solutions".

In case you're curious, the solutions are:

q = 7.5 + 5.204165·i

or

q = 7.5 - 5.204165·i

where symbol i represents the Imaginary Unit. :cool:
 
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