This question has already been answered once incorrectly, if your first answer c

Question

This question has already been answered once incorrectly, if your first answer comes out to 1600e^(-6) you are wrong.
O AT&T; LTE 6:53 PM 4% webwork.wustl.edu 4 of the questions remain unanswered (1 point) The temperature at a point (x.y,z) is given by T(x, y, z) = 200e-z?/4 9 where T is measured in degrees Celsius and x.y, and z in meters. There are lots of places to make silly errors in this problem; just try to keep track of what needs to be a unit vector. Find the rate of change of the temperature at the point (-1, -1, -1) in the direction toward the point (-3, 5, 4) (-522.222222(e (-49/36)/(sqrt(50) In which direction (unit vector) does the temperature increase the fastest at (1 What is the maximum rate of increase of T at (-1,-1, -1)? Note: You can earn nartial credit on this

Explanation / Answer

Consider the function:

             

Find the partial derivatives.

The gradient of is,

            

Then,

          

To find the rate of change of in the direction of vector joining and .

              

Find the unit vector in the direction of vector joining the points and .

                   

Therefore, the rate of change of in the direction of is,

The temperature increases fastest in the direction of .

That is, in the direction of vector .

That is, in the direction of vector .

The maximum of rate of change at is,

          

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.