Respuesta :
Answer:
a) A(x) = 360*x - 3*x²
b) The Domain of the function is ( 0 : ∞ )
c) x = 60 yards
y = 180 yards
c) A(max) = 10800 yd²
Step-by-step explanation:
Two rectangular corrals, with sides y and x ( y is the side parallel to the river) having a river as one side of the corrals means:
L length to be fenced
L = y + 3*x 360 = y + 3*x y = 360 - 3*x
The total areaof the two corrals as a function of x is
A(t) = x*y as y = 360 - 3*x by substitution we get
A(x) = x * ( 360 - 3*x)
A(x) = 360*x - 3*x²
Tacking derivatives on both sides of the equation we get:
A´(x) = 360 - 6*x A´(x) = 0 360 - 6*x = 0
x = 60 yards
and y = 360 - 3*x y = 360 - 180 y = 180 yards
A(max) = 60*180 = 10800 yd²
To find out if the value x = 60 is the x value for a maximum of A we go to the second derivative
A´´(x) = - 6 A´´(x) < 0 then there is a maximum value for function A in x = 60
The Domain of the function is ( 0 : ∞ )
