The maximum area of the patio is 300 ft², option (A).
How to determine the maximum area of the fence
The given area function is A(x) = 60x - 3x²
the critical points,is gotten by taking the derivative of the area function and set it equal to zero:
A(x) = 60x - 3x²
A'(x) = 60 - 6x
Setting A'(x) = 0, we get:
60 - 6x = 0
x = 10.
The second derivative is
A''(x) = -6,
Since the second derivative is negative at x = 10, this confirms that x = 10 is a maximum.
substitute x = 10 into the original area function to find the maximum area:
A(10) = 60(10) - 3(10)²
= 600 - 300 = 300
Therefore, the maximum area of the patio is 300 ft², option (A).
Complete question