# Math Help - Quadratic equation problem/optimization

"Sweet Harmony crafts has determined that when x hundred dulcimers are built, the average cost per dulcimer can be estimated by:
$C(x) = 0.1x^2 - 0.7x + 2.425$,
where C(x) is in hundreds of dollars. What is the minimum average cost per dulcimer and how many dulcimers should be built in order to achieve that minimum?"

Just need some guidance on how to interpret this; what I should be doing to find out the answers to the questions in bold. Thanks!

2. Differentiate the equation to get C'(x).

Then find the point where C'(x) = 0 and this will be the minimum average cost.

3. Originally Posted by Educated
Differentiate the equation to get C'(x).

Then find the point where C'(x) = 0 and this will be the minimum average cost.
Sorry man, could you explain to me what "differentiate the equation" means? I have never heard that term come up in my class or paper.

As for C(x) = 0, is that the same concept of finding the x-intercepts? (I.E.: Set $0.1x^2 - 0.7x + 2.425$ equal to $0$, then use the Quadratic Formula)

4. Originally Posted by Kyrie
Sorry man, could you explain to me what "differentiate the equation" means? I have never heard that term come up in my class or paper.

As for C(x) = 0, is that the same concept of finding the x-intercepts? (I.E.: Set $0.1x^2 - 0.7x + 2.425$ equal to $0$, then use the Quadratic Formula)
Differentiation requires some calculus. Seeing you haven't done that, for a quadratic equation of the form

$a^2x + bx + c = 0$

If a > 0, the minimum point is when x = -b/(2a)
If a < 0, -b/(2a) gives the x intercept of the maximum point.

5. Originally Posted by Kyrie
As for C(x) = 0, is that the same concept of finding the x-intercepts? (I.E.: Set $0.1x^2 - 0.7x + 2.425$ equal to $0$, then use the Quadratic Formula)
No. C'(x) isn't the same as C(x). C'(x) is the derivative of the function C(x), where C'(x) is the formula for the change in y over the change in x, which is the gradient/slope of C(x) at a given point.

Since you haven't learnt this yet, use Gusbob's method to find the minimum point.