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?

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,

asdsad

step-by-step explanation: