The temperature at a point (x, y, z) is given by T(x, y, z)= 300e-x²-sy²-92² where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature at the point P(4, -1, 4) in the direction towards the point (5, -4, 6). (-55600)e-165 14 X *C/m (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P.

The temperature at a point (x, y, z) is given by T(x, y, z)= 300e-x²-sy²-92² where T is measured in °C and x, y, z in meters. (a) Find the rate of change of temperature at the point P(4, -1, 4) in the direction towards the point (5, -4, 6). (-55600)e-165 14 X *C/m (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter7: Integration

Section7.1: Antiderivatives

Problem 46E: The slope of the tangent line to a curve is given by, f(x)=6x24x+3. If the point (0,1) is on the...

See similar textbooks

Similar questions

Find the constant of proportionality. y is directly proportional to x. If x=30, then y=15.
YOUR TURN Suppose x are y are both functions of t and x3+2xy+y2=1. If x=1, y=2, and dxdt=6, then find dydt.
Find the constant of proportionality. z is directly proportional to the sum of x and y. If x=2 and y=5, then z=28.
YOUR TURN Find dy/dx if y=5x2-6x-2.
The kinetic energy E of an object varies jointly with the object’s mass m and the square of the object’s velocity v . An object with a mass of 50 kilograms traveling at 16 meters per second has a kinetic energy of 6400 joules. What is the kinetic energy of an object with a mass of 70 kilograms traveling at 20 meters per second?
The slope of the tangent line to a curve is given by, f(x)=6x24x+3. If the point (0,1) is on the curve, find an equation of the curve.