Answer :
Answer:
There is no critical point associated with a maximum area of the triangle.
Step-by-step explanation:
From Geometry we understand that the area of the triangle is defined by the following formula:
[tex]A = \frac{1}{2}\cdot w\cdot h[/tex] (1)
Where:
[tex]A[/tex] - Area, measured in square yards.
[tex]w[/tex] - Width, measured in yards.
[tex]h[/tex] - Height, measured in yards.
From statement the following relationships are known:
[tex]w = 2\cdot x[/tex] (2)
[tex]h = 50\cdot x[/tex] (3)
By applying (2) and (3) in (1) we obtain this expression:
[tex]A = \frac{1}{2}\cdot (2\cdot x)\cdot (50\cdot x)[/tex]
[tex]A = 50\cdot x^{2}[/tex] (4)
Now we perform First and Second Derivative Test on the resulting expression:
First Derivative Test
[tex]A' = 100\cdot x[/tex] (5)
[tex]100\cdot x = 0[/tex]
[tex]x = 0\,yd[/tex]
[tex]x = 0\,yd[/tex] is a critical point of (4).
Second Derivative Test
[tex]A'' = 100[/tex] (6)
The critical point leads to an absolute minimum. According to this analysis, there is no critical values associated to maximum area.