SOLUTION: Point P (u,v) is in the first quadrant on the graph of the line connecting the points (0,4) and (4,0). A shaded triangular region is shown in the diagram. For what point P will the
Question 1152314: Point P (u,v) is in the first quadrant on the graph of the line connecting the points (0,4) and (4,0). A shaded triangular region is shown in the diagram. For what point P will the area of the shaded triangular region be a maximum? Answer by ikleyn(52779) (Show Source):
x-coordinate of the point P is "u";
y--coordinate of the point P is "v".
These coordinates satisfy equation
u + v = 4.
The area of the triangle is
S = = = = .
Thus the area "S" is the quadratic function of "u".
It achieves the maximum value at u = " " = = = 2.
The value of the maximum is S = = = = 2.
ANSWER. The area of the triangle has the maximum at the point P = (2,2), and the value of the maximum is 2.
