A foam box's length and width are increasing by 3 and 3 centimeters per minute, respectively, while its height is decreasing by 2 centimeters per minute. At the time when the box's length, width, and height are 1, 2, and 4, respectively, what is the rate of change of the length of the long diagonal of the box

The rate of change of the length of the diagonal is

Step-by-step explanation:

For the box of length , width , and height , the length of the diagonal is given by

,

Taking the time derivative of both sides we get:

since for any function

,

our equation becomes

Now, at a certain time when , the length of the diagonal is

,

and since

equation (1) becomes

or

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.