mya6137
04.12.2019 •
Mathematics
The hypotenuse of a right triangle has one end at the origin and one end on the curve y = x 2 e −3x , with x ≥ 0. one of the other two sides is on the x-axis, the other side is parallel to the y-axis. find the maximum area of such a triangle. at what x-value does it occur?
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Ответ:
At x = 1 and maximum area = 0.0499
Step-by-step explanation:
The hypotenuse of a right triangle has one end at the origin and other end on the curve, with x ≥ 0.
One leg of right triangle is x-axis and another leg parallel to y-axis.
Length of base of right triangle = x
Height of right triangle = y
Area of right triangle,
For maximum/minimum value of area.
Now, find critical point,
x =0,1
For x = 0, y = 0
For x = 1,
using double derivative test:-
At x= 0 ,
Neither maximum nor minimum
At x = 1,
Maximum area at x = 1
The maximum area of right triangle at x = 1
Maximum area,
Ответ: