# max/min problem (1 Viewer)

#### astroman

##### Well-Known Member
$\bg_white The cost per hour of a bike ride is given by the formula:\ c=x^2-15x+70\\where x is the distance travelled in Km. Find the distance that gives the minimum cost.$

#### seventhroot

##### gg no re
general steps

> diff it
> set == 0
> solve for x (answer: 15/2)
> test that it is a minimum

#### astroman

##### Well-Known Member
$\bg_white rectangle\\perimeter=60\\length=x \\area=30x-x^2\\$

how do i get the area?

#### plutonium-238

##### Member
Differentiate the area first and then let it equal to zero and solve for x. After that, sub back into A.

#### integral95

##### Well-Known Member
alternatively, you could use the formula $\bg_white x = -\frac{b}{2a}$ since you're dealing with parabolas

#### ConorDevaney

##### Member
^ if you asking how you feet from the perimeter and sides equaling zero, you make 60 (the perimeter) equal to the sums of the sides. Therefore 60 = (30 - x) + (30-x) + x +x. Therefore area = x . (30 -x). Therefre area = 30x -x^2