121616949-math.123

# 121616949-math.123 - 6.1 Optimization 109 whether this is...

This preview shows page 1. Sign up to view the full content.

6.1 Optimization 109 whether this is true. Since the left side is clearly larger than 4 · 4 which is clearly larger than 3, this settles the question.) A similar analysis shows that there is also no global minimum. The graph of f ( x ) on ( - 2 , 2) is shown in figure 6.2 . EXAMPLE 6.7 Of all rectangles of area 100, which has the smallest perimeter? First we must translate this into a purely mathematical problem in which we want to find the minimum value of a function. If x denotes one of the sides of the rectangle, then the adjacent side must be 100 /x (in order that the area be 100). So the function we want to minimize is f ( x ) = 2 x + 2 100 x since the perimeter is twice the length plus twice the width of the rectangle. Not all values of x make sense in this problem: lengths of sides of rectangles must be positive, so x > 0. If x > 0 then so is 100 /x , so we need no second condition on x . We next find f ( x ) and set it equal to zero: 0 = f ( x ) = 2 - 200 /x 2 . Solving f ( x ) = 0 for x gives us x = ± 10. We are interested only in x > 0, so only the value x = 10 is of interest. Since
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern