* Joshua Anthony Balaga wants to build a rectangular pen for his eggplant seeds. What is the biggest possible area enclosed with 40 meters of fencing material?
a. 100 sq.meters
b. 99 sq.meters
c. 96 sq.meters
d. 91 sq.meters
10
9
8
7
6
5
4
3
2
1
TIMES UP!!!
If you answered letter ‘a’ , congratulations for you are right!
Solution:
let x = width
y = length
A = x * y
P = 2x + 2y
40 = 2x + 2y
2y = 40 – 2x
y = 20 – x
A = x * y
A = x(20 –x)
A =20x – x2
Find the derivative of the area and equate it to zero, after that get the maxima.
*To test if the number is in maxima, you must get the second derivative, if it is negative, thus the answer is maxima, on the other hand, if it is positive it is minima.
dA/dx = 20 – 2x
0 = 20 – 2x
2x = 20
x = 10
Check if 10 is the maxima:
A’ = 20 -2x
A’’ = -2
Since A’’ is negative, thus positive 10 is the maxima.
A = x(20 – x)
A = 10(20 – 10)
A = 10 * 10
A = 100 sq.meters