Question 1021476
A = 40x - x^2 (note that this is a parabola that curves downward)
:
take the first derivative of A
:
A' = 40 - 2x
:
now set A' = 0 and solve for x
:
40 - 2x = 0
:
2x = 40
:
x = 20
:
A) x = 20 means the width is 20 feet
A = 40(20) - 20^2 = 400
maximum area is 400 square feet
:
B) width of 20 feet yields max area