A particle travels along the parabolic path y=x² from left to right, where x and y are in meters. The temperature at any point (x, y) in the plane is given in degrees Celsius by 40 1 + x² + y² a. What is the rate of change of the temperature experienced by the particle as it travels along the parabola at the moment the particle passes through the point (-2, 4)? (Hint: Find an appropriate directional derivative.) T(x, y) = b. Suppose the particle travels at a speed of 5 meters per second. How fast is the temperature changing with respect to time as the particle passes through the point (-2, 4)?

A particle travels along the parabolic path y=x² from left to right, where x and y are in meters. The temperature at any point (x, y) in the plane is given in degrees Celsius by 40 1 + x² + y² a. What is the rate of change of the temperature experienced by the particle as it travels along the parabola at the moment the particle passes through the point (-2, 4)? (Hint: Find an appropriate directional derivative.) T(x, y) = b. Suppose the particle travels at a speed of 5 meters per second. How fast is the temperature changing with respect to time as the particle passes through the point (-2, 4)?

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.2: Introduction To Conics: parabolas

Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.

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