Applications of Maximum or Minimum John wants to build a rectangular enclosure for his animals. One side of the pen will be against the barn, so he
needs no fence on that side. The other three sides will be enclosed with wire fencing. If John has 750 feet of
fencing, you can find the dimensions that maximize the area of the enclosure.
a) Let w be the width of the enclosure (perpendicular to the barn) and let l be the length of the enclosure
(parallel to the barn). Write an function for the area A of the enclosure in terms of w. (HINT first write two
equations with w and I and A. Solve for l in one equation and substitute for l in the other).
Aw) =
b) What width w would maximize the area?
W=
ft
c) What is the maximum area?
A =
square feet
Question Help: Read Message instructor

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!