Purchase Solution

Rate of change

Not what you're looking for?

Ask 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?

Purchase this Solution

Solution Summary

This solution shows how to find the rate of change of temperature at a given point.

Solution Preview

(a) Gradient of W =dW/dx(i)+dW/dy(j)+dW/dz(k), where (i),(j) and (k) are unit ...

Purchase this Solution


Free BrainMass Quizzes
Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.