Martha needs her vape

Question

Martha is fencing off a small herb garden in her backyard. If she has 20 feet of fencing and wants a rectangular garden, what length and width will give her the largest area? Draw the graph of the function for the area in terms of width and determine the maximum.

Answer 1

5 by 5 feet give maximum area. 20/4 sides = 5 feet per side

A square gives maximum area for a given perimeter

Area = A = WL

20=2(W+L) = 2W +2L

2W = 20-2L

W = 10-L

A=WL = (10-L)L = 10L -L^2

take the derivative and set equal to zero, then solve for L

A'(L) = 10-2L=0

2L = 10

L = 10/2 =5

W =10-5 = 5

A =10L-L^2 graphically is a downward opening parabola like y=-x^2 +10x or

y =-(x^2 -10x + 25) +25

y =-(x-5)^2 +25 where vertex= (5,25) and y intercept = 0, x intercepts = 0 and -10

Put L on the x axis and A on the vertical axis

You could have used either L or W on the x axis