Rate of change
Not what you're looking for? Search our solutions OR ask your own Custom question.
Suppose that the temperature at the point (x, y, z) in space (in degrees Celsius) is given by the formula: W= 100 - x^2 - y^2 - z^2. The units in space are meters. (a) Find the rate of change of temperature at the point P(3, -4, 5) in the direction of the vector v=3i - 4j + 12k. (b) In what direction does W increase most rapidly at P? What is the value of the maximal directional derivative at P?
© BrainMass Inc. brainmass.com December 15, 2022, 4:14 pm ad1c9bdddfhttps://brainmass.com/math/derivatives/rate-change-temperature-point-13787
Solution Preview
(a) Gradient of W =dW/dx(i)+dW/dy(j)+dW/dz(k), where (i),(j) and (k) are unit ...
Solution Summary
This solution shows how to find the rate of change of temperature at a given point.
$2.49