Respuesta :
Answer:
Maximum area of the rectangular park is 75 square yards.
Step-by-step explanation:
The function A(x) = -x(10 - x) describes the area of a rectangular flower garden.
A(x) = -x(10 - x)
Where x = width of the garden
For the maximum area we will find the derivative of the given function and equate it to zero.
[tex]\frac{dA}{dx}=0[/tex]
[tex]\frac{dA}{dx}=\frac{d}{dx}[-x(10-x)][/tex] = 0
[tex]A'(x)=-10+2x[/tex]
For A'(x) = 0,
2x - 10 = 0
x = 5 yards
For A(5) = 5(10 + 5)
= 75 square yards
Therefore, the maximum area of the rectangular garden is 75 yards².
Answer:
No, maxima point found!
Step-by-step explanation:
Given function:
[tex]A(x)=-x(10-x)[/tex]
where:
A = area of rectangular flower garden
x= side of rectangle
Now for the function to yield extrema:
[tex]\frac{d}{dx}(A) =0[/tex]
[tex]\frac{d}{dx} (-10x+x^2)=0[/tex]
[tex]-10+2x=0[/tex]
[tex]x=5[/tex] will be the point of extrema.
Now we check for second derivative A" at x=5:
[tex]A"=\frac{d}{dx} (A')[/tex]
[tex]A"=x[/tex]
[tex]A"=5>0[/tex] so it yields minima at this point and hence we do not have a maxima for this function.
