Respuesta :
Using implicit differentiation, it is found that the rate of change is of the width is of -3 feet/min.
What is the area of a rectangle?
The area of a rectangle of length l and height h is given by:
[tex]A = lh[/tex]
Applying implicit differentiation, the rate of change is given by:
[tex]\frac{dA}{dt} = l\frac{dh}{dt} + h\frac{dl}{dt}[/tex]
In this problem, we have that:
- The area is constant, hence [tex]\frac{dA}{dt} = 0[/tex].
- Area of 2 square feet, height of 2 feet, hence [tex]h = 2, lh = 2 \rightarrow l = 1[/tex].
- The height is changing at a rate of 6 feet/minute, hence [tex]\frac{dh}{dt} = 6[/tex].
Then:
[tex]\frac{dA}{dt} = l\frac{dh}{dt} + h\frac{dl}{dt}[/tex]
[tex]0 = 6 + 2\frac{dl}{dt}[/tex]
[tex]2\frac{dl}{dt} = -6[/tex]
[tex]\frac{dl}{dt} = -3[/tex]
The rate of change is of the width is of -3 feet/min.
To learn more about implicit differentiation, you can take a look at https://brainly.com/question/25608353
